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Documents authored by Liu, C. H. Bryan

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Liu, C. H. Bryan

Document
DOI: 10.4230/OASIcs.ICCSW.2018.1
Speeding Up BigClam Implementation on SNAP

Authors: C. H. Bryan Liu and Benjamin Paul Chamberlain

Published in: OASIcs, Volume 66, 2018 Imperial College Computing Student Workshop (ICCSW 2018)

Abstract
We perform a detailed analysis of the C++ implementation of the Cluster Affiliation Model for Big Networks (BigClam) on the Stanford Network Analysis Project (SNAP). BigClam is a popular graph mining algorithm that is capable of finding overlapping communities in networks containing millions of nodes. Our analysis shows a key stage of the algorithm - determining if a node belongs to a community - dominates the runtime of the implementation, yet the computation is not parallelized. We show that by parallelizing computations across multiple threads using OpenMP we can speed up the algorithm by 5.3 times when solving large networks for communities, while preserving the integrity of the program and the result.
Cite as

C. H. Bryan Liu and Benjamin Paul Chamberlain. Speeding Up BigClam Implementation on SNAP. In 2018 Imperial College Computing Student Workshop (ICCSW 2018). Open Access Series in Informatics (OASIcs), Volume 66, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{liu_et_al:OASIcs.ICCSW.2018.1,
  author =	{Liu, C. H. Bryan and Chamberlain, Benjamin Paul},
  title =	{{Speeding Up BigClam Implementation on SNAP}},
  booktitle =	{2018 Imperial College Computing Student Workshop (ICCSW 2018)},
  pages =	{1:1--1:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-097-2},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{66},
  editor =	{Pirovano, Edoardo and Graversen, Eva},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2018.1},
  URN =		{urn:nbn:de:0030-drops-101829},
  doi =		{10.4230/OASIcs.ICCSW.2018.1},
  annote =	{Keywords: BigClam, Community Detection, Parallelization, Networks}
}

Liu, Quanquan C.

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.28
Scalable Auction Algorithms for Bipartite Maximum Matching Problems

Authors: Quanquan C. Liu, Yiduo Ke, and Samir Khuller

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
Bipartite maximum matching and its variants are well-studied problems under various models of computation with the vast majority of approaches centering around various methods to find and eliminate augmenting paths. Beginning with the seminal papers of Demange, Gale and Sotomayor [DGS86] and Bertsekas [Ber81], bipartite maximum matching problems have also been studied in the context of auction algorithms. These algorithms model the maximum matching problem as an auction where one side of the bipartite graph consists of bidders and the other side consists of items; as such, these algorithms offer a very different approach to solving this problem that do not use classical methods. Dobzinski, Nisan and Oren [DNO14] demonstrated the utility of such algorithms in distributed, interactive settings by providing a simple and elegant O(log n/ε²) round maximum cardinality bipartite matching (MCM) algorithm that has small round and communication complexity and gives a (1-ε)-approximation for any (not necessarily constant) ε > 0. They leave as an open problem whether an auction algorithm, with similar guarantees, can be found for the maximum weighted bipartite matching (MWM) problem. Very recently, Assadi, Liu, and Tarjan [ALT21] extended the utility of auction algorithms for MCM into the semi-streaming and massively parallel computation (MPC) models, by cleverly using maximal matching as a subroutine, to give a new auction algorithm that uses O(1/ε²) rounds and achieves the state-of-the-art bipartite MCM results in the streaming and MPC settings. In this paper, we give new auction algorithms for maximum weighted bipartite matching (MWM) and maximum cardinality bipartite b-matching (MCbM). Our algorithms run in O(log n/ε⁸) and O(log n/ε²) rounds, respectively, in the distributed setting. We show that our MWM algorithm can be implemented in the distributed, interactive setting using O(log² n) and O(log n) bit messages, respectively, directly answering the open question posed by Demange, Gale and Sotomayor [DNO14]. Furthermore, we implement our algorithms in a variety of other models including the the semi-streaming model, the shared-memory work-depth model, and the massively parallel computation model. Our semi-streaming MWM algorithm uses O(1/ε⁸) passes in O(n log n ⋅ log(1/ε)) space and our MCbM algorithm runs in O(1/ε²) passes using O((∑_{i ∈ L} b_i + |R|) log(1/ε)) space (where parameters b_i represent the degree constraints on the b-matching and L and R represent the left and right side of the bipartite graph, respectively). Both of these algorithms improves exponentially the dependence on ε in the space complexity in the semi-streaming model against the best-known algorithms for these problems, in addition to improvements in round complexity for MCbM. Finally, our algorithms eliminate the large polylogarithmic dependence on n in depth and number of rounds in the work-depth and massively parallel computation models, respectively, improving on previous results which have large polylogarithmic dependence on n (and exponential dependence on ε in the MPC model).
Cite as

Quanquan C. Liu, Yiduo Ke, and Samir Khuller. Scalable Auction Algorithms for Bipartite Maximum Matching Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 28:1-28:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{liu_et_al:LIPIcs.APPROX/RANDOM.2023.28,
  author =	{Liu, Quanquan C. and Ke, Yiduo and Khuller, Samir},
  title =	{{Scalable Auction Algorithms for Bipartite Maximum Matching Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{28:1--28:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.28},
  URN =		{urn:nbn:de:0030-drops-188537},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.28},
  annote =	{Keywords: auction algorithms, maximum weight bipartite matching, maximum b-matching, distributed blackboard model, parallel work-depth model, streaming model, massively parallel computation model}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.52
Triangle Counting with Local Edge Differential Privacy

Authors: Talya Eden, Quanquan C. Liu, Sofya Raskhodnikova, and Adam Smith

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Many deployments of differential privacy in industry are in the local model, where each party releases its private information via a differentially private randomizer. We study triangle counting in the noninteractive and interactive local model with edge differential privacy (that, intuitively, requires that the outputs of the algorithm on graphs that differ in one edge be indistinguishable). In this model, each party’s local view consists of the adjacency list of one vertex. In the noninteractive model, we prove that additive Ω(n²) error is necessary, where n is the number of nodes. This lower bound is our main technical contribution. It uses a reconstruction attack with a new class of linear queries and a novel mix-and-match strategy of running the local randomizers with different completions of their adjacency lists. It matches the additive error of the algorithm based on Randomized Response, proposed by Imola, Murakami and Chaudhuri (USENIX2021) and analyzed by Imola, Murakami and Chaudhuri (CCS2022) for constant ε. We use a different postprocessing of Randomized Response and provide tight bounds on the variance of the resulting algorithm. In the interactive setting, we prove a lower bound of Ω(n^{3/2}) on the additive error. Previously, no hardness results were known for interactive, edge-private algorithms in the local model, except for those that follow trivially from the results for the central model. Our work significantly improves on the state of the art in differentially private graph analysis in the local model.
Cite as

Talya Eden, Quanquan C. Liu, Sofya Raskhodnikova, and Adam Smith. Triangle Counting with Local Edge Differential Privacy. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 52:1-52:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{eden_et_al:LIPIcs.ICALP.2023.52,
  author =	{Eden, Talya and Liu, Quanquan C. and Raskhodnikova, Sofya and Smith, Adam},
  title =	{{Triangle Counting with Local Edge Differential Privacy}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{52:1--52:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.52},
  URN =		{urn:nbn:de:0030-drops-181048},
  doi =		{10.4230/LIPIcs.ICALP.2023.52},
  annote =	{Keywords: local differential privacy, reconstruction attacks, lower bounds, triangle counting}
}
Document
DOI: 10.4230/LIPIcs.FORC.2023.8
An Algorithmic Approach to Address Course Enrollment Challenges

Authors: Arpita Biswas, Yiduo Ke, Samir Khuller, and Quanquan C. Liu

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract
Massive surges of enrollments in courses have led to a crisis in several computer science departments - not only is the demand for certain courses extremely high from majors, but the demand from non-majors is also very high. Much of the time, this leads to significant frustration on the part of the students, and getting seats in desired courses is a rather ad-hoc process. One approach is to first collect information from students about which courses they want to take and to develop optimization models for assigning students to available seats in a fair manner. What makes this problem complex is that the courses themselves have time conflicts, and the students have credit caps (an upper bound on the number of courses they would like to enroll in). We model this problem as follows. We have n agents (students), and there are "resources" (these correspond to courses). Each agent is only interested in a subset of the resources (courses of interest), and each resource can only be assigned to a bounded number of agents (available seats). In addition, each resource corresponds to an interval of time, and the objective is to assign non-overlapping resources to agents so as to produce "fair and high utility" schedules. In this model, we provide a number of results under various settings and objective functions. Specifically, in this paper, we consider the following objective functions: total utility, max-min (Santa Claus objective), and envy-freeness. The total utility objective function maximizes the sum of the utilities of all courses assigned to students. The max-min objective maximizes the minimum utility obtained by any student. Finally, envy-freeness ensures that no student envies another student’s allocation. Under these settings and objective functions, we show a number of theoretical results. Specifically, we show that the course allocation under the time conflicts problem is NP-complete but becomes polynomial-time solvable when given only a constant number of students or all credits, course lengths, and utilities are uniform. Furthermore, we give a near-linear time algorithm for obtaining a constant 1/2-factor approximation for the general maximizing total utility problem when utility functions are binary. In addition, we show that there exists a near-linear time algorithm that obtains a 1/2-factor approximation on total utility and a 1/4-factor approximation on max-min utility when given uniform credit caps and uniform utilities. For the setting of binary valuations, we show three polynomial time algorithms for 1/2-factor approximation of total utility, envy-freeness up to one item, and a constant factor approximation of the max-min utility value when course lengths are within a constant factor of each other. Finally, we conclude with experimental results that demonstrate that our algorithms yield high-quality results in real-world settings.
Cite as

Arpita Biswas, Yiduo Ke, Samir Khuller, and Quanquan C. Liu. An Algorithmic Approach to Address Course Enrollment Challenges. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{biswas_et_al:LIPIcs.FORC.2023.8,
  author =	{Biswas, Arpita and Ke, Yiduo and Khuller, Samir and Liu, Quanquan C.},
  title =	{{An Algorithmic Approach to Address Course Enrollment Challenges}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.8},
  URN =		{urn:nbn:de:0030-drops-179297},
  doi =		{10.4230/LIPIcs.FORC.2023.8},
  annote =	{Keywords: fairness, allocation, matching, algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.39
Massively Parallel Algorithms for Small Subgraph Counting

Authors: Amartya Shankha Biswas, Talya Eden, Quanquan C. Liu, Ronitt Rubinfeld, and Slobodan Mitrović

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel Computation (MPC) model is the de-facto standard for studying graph algorithms in these frameworks theoretically. Subgraph counting is one such fundamental problem in analyzing massive graphs, with the main algorithmic challenges centering on designing methods which are both scalable and accurate. Given a graph G = (V, E) with n vertices, m edges and T triangles, our first result is an algorithm that outputs a (1+ε)-approximation to T, with asymptotically optimal round and total space complexity provided any S ≥ max{(√ m, n²/m)} space per machine and assuming T = Ω(√{m/n}). Our result gives a quadratic improvement on the bound on T over previous works. We also provide a simple extension of our result to counting any subgraph of k size for constant k ≥ 1. Our second result is an O_δ(log log n)-round algorithm for exactly counting the number of triangles, whose total space usage is parametrized by the arboricity α of the input graph. We extend this result to exactly counting k-cliques for any constant k. Finally, we prove that a recent result of Bera, Pashanasangi and Seshadhri (ITCS 2020) for exactly counting all subgraphs of size at most 5 can be implemented in the MPC model in Õ_δ(√{log n}) rounds, O(n^δ) space per machine and O(mα³) total space. In addition to our theoretical results, we simulate our triangle counting algorithms in real-world graphs obtained from the Stanford Network Analysis Project (SNAP) database. Our results show that both our approximate and exact counting algorithms exhibit improvements in terms of round complexity and approximation ratio, respectively, compared to two previous widely used algorithms for these problems.
Cite as

Amartya Shankha Biswas, Talya Eden, Quanquan C. Liu, Ronitt Rubinfeld, and Slobodan Mitrović. Massively Parallel Algorithms for Small Subgraph Counting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 39:1-39:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biswas_et_al:LIPIcs.APPROX/RANDOM.2022.39,
  author =	{Biswas, Amartya Shankha and Eden, Talya and Liu, Quanquan C. and Rubinfeld, Ronitt and Mitrovi\'{c}, Slobodan},
  title =	{{Massively Parallel Algorithms for Small Subgraph Counting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{39:1--39:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.39},
  URN =		{urn:nbn:de:0030-drops-171619},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.39},
  annote =	{Keywords: triangle counting, massively parallel computation, clique counting, approximation algorithms, subgraph counting}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.47
Scheduling with Communication Delay in Near-Linear Time

Authors: Quanquan C. Liu, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We consider the problem of efficiently scheduling jobs with precedence constraints on a set of identical machines in the presence of a uniform communication delay. Such precedence-constrained jobs can be modeled as a directed acyclic graph, G = (V, E). In this setting, if two precedence-constrained jobs u and v, with v dependent on u (u ≺ v), are scheduled on different machines, then v must start at least ρ time units after u completes. The scheduling objective is to minimize makespan, i.e. the total time from when the first job starts to when the last job finishes. The focus of this paper is to provide an efficient approximation algorithm with near-linear running time. We build on the algorithm of Lepere and Rapine [STACS 2002] for this problem to give an O((ln ρ)/(ln ln ρ))-approximation algorithm that runs in Õ(|V|+|E|) time.
Cite as

Quanquan C. Liu, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Scheduling with Communication Delay in Near-Linear Time. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 47:1-47:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.STACS.2022.47,
  author =	{Liu, Quanquan C. and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.},
  title =	{{Scheduling with Communication Delay in Near-Linear Time}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{47:1--47:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.47},
  URN =		{urn:nbn:de:0030-drops-158570},
  doi =		{10.4230/LIPIcs.STACS.2022.47},
  annote =	{Keywords: near-linear time scheduling, scheduling with duplication, precedence-constrained jobs, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.7
Near-Optimal Distributed Implementations of Dynamic Algorithms for Symmetry Breaking Problems

Authors: Shiri Antaki, Quanquan C. Liu, and Shay Solomon

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main quality measure of an algorithm is its update time, i.e. the time needed to restore the solution after each update. While real-life networks are very often distributed across multiple machines, the fundamental question of finding efficient dynamic, distributed graph algorithms received little attention to date. The goal in this setting is to optimize both the round and message complexities incurred per update step, ideally achieving a message complexity that matches the centralized update time in O(1) (perhaps amortized) rounds. Toward initiating a systematic study of dynamic, distributed algorithms, we study some of the most central symmetry-breaking problems: maximal independent set (MIS), maximal matching/(approx-) maximum cardinality matching (MM/MCM), and (Δ + 1)-vertex coloring. This paper focuses on dynamic, distributed algorithms that are deterministic, and in particular - robust against an adaptive adversary. Most of our focus is on our MIS algorithm, which achieves O (m^{2/3}log² n) amortized messages in O(log² n) amortized rounds in the Congest model. Notably, the amortized message complexity of our algorithm matches the amortized update time of the best-known deterministic centralized MIS algorithm by Gupta and Khan [SOSA'21] up to a polylog n factor. The previous best deterministic distributed MIS algorithm, by Assadi et al. [STOC'18], uses O(m^{3/4}) amortized messages in O(1) amortized rounds, i.e., we achieve a polynomial improvement in the message complexity by a polylog n increase to the round complexity; moreover, the algorithm of Assadi et al. makes an implicit assumption that the network is connected at all times, which seems excessively strong when it comes to dynamic networks. Using techniques similar to the ones we developed for our MIS algorithm, we also provide deterministic algorithms for MM, approximate MCM and (Δ + 1)-vertex coloring whose message complexities match or nearly match the update times of the best centralized algorithms, while having either constant or polylog(n) round complexities.
Cite as

Shiri Antaki, Quanquan C. Liu, and Shay Solomon. Near-Optimal Distributed Implementations of Dynamic Algorithms for Symmetry Breaking Problems. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 7:1-7:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{antaki_et_al:LIPIcs.ITCS.2022.7,
  author =	{Antaki, Shiri and Liu, Quanquan C. and Solomon, Shay},
  title =	{{Near-Optimal Distributed Implementations of Dynamic Algorithms for Symmetry Breaking Problems}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{7:1--7:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.7},
  URN =		{urn:nbn:de:0030-drops-156039},
  doi =		{10.4230/LIPIcs.ITCS.2022.7},
  annote =	{Keywords: dynamic graph algorithms, distributed algorithms, symmetry breaking problems, maximal independent set, matching, coloring}
}
Document
DOI: 10.4230/LIPIcs.DISC.2021.39
The Power of Random Symmetry-Breaking in Nakamoto Consensus

Authors: Lili Su, Quanquan C. Liu, and Neha Narula

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
Nakamoto consensus underlies the security of many of the world’s largest cryptocurrencies, such as Bitcoin and Ethereum. Common lore is that Nakamoto consensus only achieves consistency and liveness under a regime where the difficulty of its underlying mining puzzle is very high, negatively impacting overall throughput and latency. In this work, we study Nakamoto consensus under a wide range of puzzle difficulties, including very easy puzzles. We first analyze an adversary-free setting and show that, surprisingly, the common prefix of the blockchain grows quickly even with easy puzzles. In a setting with adversaries, we provide a small backwards-compatible change to Nakamoto consensus to achieve consistency and liveness with easy puzzles. Our insight relies on a careful choice of symmetry-breaking strategy, which was significantly underestimated in prior work. We introduce a new method - coalescing random walks - to analyzing the correctness of Nakamoto consensus under the uniformly-at-random symmetry-breaking strategy. This method is more powerful than existing analysis methods that focus on bounding the number of convergence opportunities.
Cite as

Lili Su, Quanquan C. Liu, and Neha Narula. The Power of Random Symmetry-Breaking in Nakamoto Consensus. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{su_et_al:LIPIcs.DISC.2021.39,
  author =	{Su, Lili and Liu, Quanquan C. and Narula, Neha},
  title =	{{The Power of Random Symmetry-Breaking in Nakamoto Consensus}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.39},
  URN =		{urn:nbn:de:0030-drops-148413},
  doi =		{10.4230/LIPIcs.DISC.2021.39},
  annote =	{Keywords: Nakamoto consensus, Byzantine consensus, blockchain, symmetry-breaking, coalescing random walks}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.1
Tatamibari Is NP-Complete

Authors: Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an m x n grid of cells, where each cell possibly contains a clue among ⊞, ⊟, ◫. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing ⊞ are square, rectangles containing ⊟ are strictly longer horizontally than vertically, rectangles containing ◫ are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
Cite as

Aviv Adler, Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Quanquan C. Liu, and Jayson Lynch. Tatamibari Is NP-Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{adler_et_al:LIPIcs.FUN.2021.1,
  author =	{Adler, Aviv and Bosboom, Jeffrey and Demaine, Erik D. and Demaine, Martin L. and Liu, Quanquan C. and Lynch, Jayson},
  title =	{{Tatamibari Is NP-Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.1},
  URN =		{urn:nbn:de:0030-drops-127624},
  doi =		{10.4230/LIPIcs.FUN.2021.1},
  annote =	{Keywords: Nikoli puzzles, NP-hardness, rectangle covering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.37
Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Authors: Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback Vertex Set, Minimum Maximal Matching, Chromatic Number, (l-)Dominating Set, Edge (l-)Dominating Set, and Connected Dominating Set. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log{n})-approximation and a bicriteria (4,4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w}))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w} * log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P != NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC).
Cite as

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel. Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{demaine_et_al:LIPIcs.ESA.2019.37,
  author =	{Demaine, Erik D. and Goodrich, Timothy D. and Kloster, Kyle and Lavallee, Brian and Liu, Quanquan C. and Sullivan, Blair D. and Vakilian, Ali and van der Poel, Andrew},
  title =	{{Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.37},
  URN =		{urn:nbn:de:0030-drops-111583},
  doi =		{10.4230/LIPIcs.ESA.2019.37},
  annote =	{Keywords: structural rounding, graph editing, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.34
Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy

Authors: Erik D. Demaine, Andrea Lincoln, Quanquan C. Liu, Jayson Lynch, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why the Longest Common Subsequence problem gets a savings of a factor of the size of cache times the length of a cache line, but no more. We take the reductions and techniques from complexity and fine-grained complexity and apply them to the I/O model to generate new (conditional) lower bounds as well as new faster algorithms. We also prove the existence of a time hierarchy for the I/O model, which motivates the fine-grained reductions. - Using fine-grained reductions, we give an algorithm for distinguishing 2 vs. 3 diameter and radius that runs in O(|E|^2/(MB)) cache misses, which for sparse graphs improves over the previous O(|V|^2/B) running time. - We give new reductions from radius and diameter to Wiener index and median. These reductions are new in both the RAM and I/O models. - We show meaningful reductions between problems that have linear-time solutions in the RAM model. The reductions use low I/O complexity (typically O(n/B)), and thus help to finely capture between "I/O linear time" O(n/B) and RAM linear time O(n). - We generate new I/O assumptions based on the difficulty of improving sparse graph problem running times in the I/O model. We create conjectures that the current best known algorithms for Single Source Shortest Paths (SSSP), diameter, and radius are optimal. - From these I/O-model assumptions, we show that many of the known reductions in the word-RAM model can naturally extend to hold in the I/O model as well (e.g., a lower bound on the I/O complexity of Longest Common Subsequence that matches the best known running time). - We prove an analog of the Time Hierarchy Theorem in the I/O model, further motivating the study of fine-grained algorithmic differences.
Cite as

Erik D. Demaine, Andrea Lincoln, Quanquan C. Liu, Jayson Lynch, and Virginia Vassilevska Williams. Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 34:1-34:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demaine_et_al:LIPIcs.ITCS.2018.34,
  author =	{Demaine, Erik D. and Lincoln, Andrea and Liu, Quanquan C. and Lynch, Jayson and Vassilevska Williams, Virginia},
  title =	{{Fine-grained I/O Complexity via Reductions: New Lower Bounds, Faster Algorithms, and a Time Hierarchy}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{34:1--34:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.34},
  URN =		{urn:nbn:de:0030-drops-83335},
  doi =		{10.4230/LIPIcs.ITCS.2018.34},
  annote =	{Keywords: IO model, Fine-grained Complexity, Algorithms}
}

Liu, Jingcheng

Document
DOI: 10.4230/LIPIcs.ITCS.2019.55
Fisher Zeros and Correlation Decay in the Ising Model

Authors: Jingcheng Liu, Alistair Sinclair, and Piyush Srivastava

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
The Ising model originated in statistical physics as a means of studying phase transitions in magnets, and has been the object of intensive study for almost a century. Combinatorially, it can be viewed as a natural distribution over cuts in a graph, and it has also been widely studied in computer science, especially in the context of approximate counting and sampling. In this paper, we study the complex zeros of the partition function of the Ising model, viewed as a polynomial in the "interaction parameter"; these are known as Fisher zeros in light of their introduction by Fisher in 1965. While the zeros of the partition function as a polynomial in the "field" parameter have been extensively studied since the classical work of Lee and Yang, comparatively little is known about Fisher zeros. Our main result shows that the zero-field Ising model has no Fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay. In addition to shedding light on Fisher zeros themselves, this result also establishes a formal connection between two distinct notions of phase transition for the Ising model: the absence of complex zeros (analyticity of the free energy, or the logarithm of the partition function) and decay of correlations with distance. We also discuss the consequences of our result for efficient deterministic approximation of the partition function. Our proof relies heavily on algorithmic techniques, notably Weitz's self-avoiding walk tree, and as such belongs to a growing body of work that uses algorithmic methods to resolve classical questions in statistical physics.
Cite as

Jingcheng Liu, Alistair Sinclair, and Piyush Srivastava. Fisher Zeros and Correlation Decay in the Ising Model. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 55:1-55:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{liu_et_al:LIPIcs.ITCS.2019.55,
  author =	{Liu, Jingcheng and Sinclair, Alistair and Srivastava, Piyush},
  title =	{{Fisher Zeros and Correlation Decay in the Ising Model}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{55:1--55:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.55},
  URN =		{urn:nbn:de:0030-drops-101483},
  doi =		{10.4230/LIPIcs.ITCS.2019.55},
  annote =	{Keywords: Ising model, zeros of polynomials, partition functions, approximate counting, phase transitions}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.843
The Complexity of Ferromagnetic Two-spin Systems with External Fields

Authors: Jingcheng Liu, Pinyan Lu, and Chihao Zhang

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS) for the special ferromagnetic Ising model with any given uniform external field. Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we allow inconsistent external fields on different nodes. In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard, even if the external field is uniform.
Cite as

Jingcheng Liu, Pinyan Lu, and Chihao Zhang. The Complexity of Ferromagnetic Two-spin Systems with External Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 843-856, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{liu_et_al:LIPIcs.APPROX-RANDOM.2014.843,
  author =	{Liu, Jingcheng and Lu, Pinyan and Zhang, Chihao},
  title =	{{The Complexity of Ferromagnetic Two-spin Systems with External Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{843--856},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.843},
  URN =		{urn:nbn:de:0030-drops-47428},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.843},
  annote =	{Keywords: Spin System, #BIS-hard, FPRAS}
}

Liu, Chih-Hung

Document
DOI: 10.4230/LIPIcs.STACS.2023.37
Approximate Selection with Unreliable Comparisons in Optimal Expected Time

Authors: Shengyu Huang, Chih-Hung Liu, and Daniel Rutschmann

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Given n elements, an integer k ≤ n/2 and a parameter ε ≥ 1/n, we study the problem of selecting an element with rank in (k-nε, k+nε] using unreliable comparisons where the outcome of each comparison is incorrect independently with a constant error probability, and multiple comparisons between the same pair of elements are independent. In this fault model, the fundamental problems of finding the minimum, selecting the k-th smallest element and sorting have been shown to require Θ(n log 1/Q), Θ(n log k/Q) and Θ(n log n/Q) comparisons, respectively, to achieve success probability 1-Q [Uriel Feige et al., 1994]. Considering the increasing complexity of modern computing, it is of great interest to develop approximation algorithms that enable a trade-off between the solution quality and the number of comparisons. In particular, approximation algorithms would even be able to attain a sublinear number of comparisons. Very recently, Leucci and Liu [Stefano Leucci and Chih-Hung Liu, 2022] proved that the approximate minimum selection problem, which covers the case that k ≤ nε, requires expected Θ(ε^{-1} log 1/Q) comparisons, but the general case, i.e., for nε < k ≤ n/2, is still open. We develop a randomized algorithm that performs expected O(k/n ε^{-2} log 1/Q) comparisons to achieve success probability at least 1-Q. For k = n ε, the number of comparisons is O(ε^{-1} log 1/Q), matching Leucci and Liu’s result [Stefano Leucci and Chih-Hung Liu, 2022], whereas for k = n/2 (i.e., approximating the median), the number of comparisons is O(ε^{-2} log 1/Q). We also prove that even in the absence of comparison faults, any randomized algorithm with success probability at least 1-Q performs expected Ω(min{n, k/n ε^{-2} log 1/Q}) comparisons. As long as n is large enough, i.e., when n = Ω(k/n ε^{-2} log 1/Q), our lower bound demonstrates the optimality of our algorithm, which covers the possible range of attaining a sublinear number of comparisons. Surprisingly, for constant Q, our algorithm performs expected O(k/n ε^{-2}) comparisons, matching the best possible approximation algorithm in the absence of computation faults. In contrast, for the exact selection problem, the expected number of comparisons is Θ(n log k) with faults versus Θ(n) without faults. Our results also indicate a clear distinction between approximating the minimum and approximating the k-th smallest element, which holds even for the high probability guarantee, e.g., if k = n/2, Q = 1/n and ε = n^{-α} for α ∈ (0, 1/2), the asymptotic difference is almost quadratic, i.e., Θ̃(n^α) versus Θ̃(n^{2α}).
Cite as

Shengyu Huang, Chih-Hung Liu, and Daniel Rutschmann. Approximate Selection with Unreliable Comparisons in Optimal Expected Time. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 37:1-37:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{huang_et_al:LIPIcs.STACS.2023.37,
  author =	{Huang, Shengyu and Liu, Chih-Hung and Rutschmann, Daniel},
  title =	{{Approximate Selection with Unreliable Comparisons in Optimal Expected Time}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{37:1--37:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.37},
  URN =		{urn:nbn:de:0030-drops-176898},
  doi =		{10.4230/LIPIcs.STACS.2023.37},
  annote =	{Keywords: Approximate Selection, Unreliable Comparisons, Independent Faults}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.64
Dual-Mode Greedy Algorithms Can Save Energy

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna, and Guido Proietti

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
In real world applications, important resources like energy are saved by deliberately using so-called low-cost operations that are less reliable. Some of these approaches are based on a dual mode technology where it is possible to choose between high-energy operations (always correct) and low-energy operations (prone to errors), and thus enable to trade energy for correctness. In this work we initiate the study of algorithms for solving optimization problems that in their computation are allowed to choose between two types of operations: high-energy comparisons (always correct but expensive) and low-energy comparisons (cheaper but prone to errors). For the errors in low-energy comparisons, we assume the persistent setting, which usually makes it impossible to achieve optimal solutions without high-energy comparisons. We propose to study a natural complexity measure which accounts for the number of operations of either type separately. We provide a new family of algorithms which, for a fairly large class of maximization problems, return a constant approximation using only polylogarithmic many high-energy comparisons and only O(n log n) low-energy comparisons. This result applies to the class of p-extendible system s [Mestre, 2006], which includes several NP-hard problems and matroids as a special case (p=1). These algorithmic solutions relate to some fundamental aspects studied earlier in different contexts: (i) the approximation guarantee when only ordinal information is available to the algorithm; (ii) the fact that even such ordinal information may be erroneous because of low-energy comparisons and (iii) the ability to approximately sort a sequence of elements when comparisons are subject to persistent errors. Finally, our main result is quite general and can be parametrized and adapted to other error models.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna, and Guido Proietti. Dual-Mode Greedy Algorithms Can Save Energy. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 64:1-64:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{geissmann_et_al:LIPIcs.ISAAC.2019.64,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo and Proietti, Guido},
  title =	{{Dual-Mode Greedy Algorithms Can Save Energy}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{64:1--64:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.64},
  URN =		{urn:nbn:de:0030-drops-115604},
  doi =		{10.4230/LIPIcs.ISAAC.2019.64},
  annote =	{Keywords: matroids, p-extendible systems, greedy algorithm, approximation algorithms, high-low energy}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.49
Optimal Sorting with Persistent Comparison Errors

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We consider the problem of sorting n elements in the case of persistent comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability p, and comparisons cannot be repeated (Braverman and Mossel, SODA'08). Sorting perfectly in this model is impossible, and the objective is to minimize the dislocation of each element in the output sequence, that is, the difference between its true rank and its position. Existing lower bounds for this problem show that no algorithm can guarantee, with high probability, maximum dislocation and total dislocation better than Omega(log n) and Omega(n), respectively, regardless of its running time. In this paper, we present the first O(n log n)-time sorting algorithm that guarantees both O(log n) maximum dislocation and O(n) total dislocation with high probability. This settles the time complexity of this problem and shows that comparison errors do not increase its computational difficulty: a sequence with the best possible dislocation can be obtained in O(n log n) time and, even without comparison errors, Omega(n log n) time is necessary to guarantee such dislocation bounds. In order to achieve this optimality result, we solve two sub-problems in the persistent error comparisons model, and the respective methods have their own merits for further application. One is how to locate a position in which to insert an element in an almost-sorted sequence having O(log n) maximum dislocation in such a way that the dislocation of the resulting sequence will still be O(log n). The other is how to simultaneously insert m elements into an almost sorted sequence of m different elements, such that the resulting sequence of 2m elements remains almost sorted.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Optimal Sorting with Persistent Comparison Errors. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{geissmann_et_al:LIPIcs.ESA.2019.49,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Optimal Sorting with Persistent Comparison Errors}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.49},
  URN =		{urn:nbn:de:0030-drops-111706},
  doi =		{10.4230/LIPIcs.ESA.2019.49},
  annote =	{Keywords: approximate sorting, comparison errors, persistent errors}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.70
Resilient Dictionaries for Randomly Unreliable Memory

Authors: Stefano Leucci, Chih-Hung Liu, and Simon Meierhans

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We study the problem of designing a dictionary data structure that is resilient to memory corruptions. Our error model is a variation of the faulty RAM model in which, except for constant amount of definitely reliable memory, each memory word is randomly unreliable with a probability p < 1/2, and the locations of the unreliable words are unknown to the algorithm. An adversary observes the whole memory and can, at any time, arbitrarily corrupt (i.e., modify) the contents of one or more unreliable words. Our dictionary has capacity n, stores N<n keys in the optimal O(N) amount of space, supports insertions and deletions in O(log n) amortized time, and allows to search for a key in O(log n) worst-case time. With a global probability of at least 1-1/n, all possible search operations are guaranteed to return the correct answer w.r.t. the set of uncorrupted keys. The closest related results are the ones of Finocchi et al. [Irene Finocchi et al., 2009] and Brodal et al. [Brodal et al., 2007] on the faulty RAM model, in which all but O(1) memory is unreliable. There, if an upper bound delta on the number of corruptions is known in advance, all dictionary operations can be implemented in Theta(log n + delta) amortized time, thus trading resiliency for speed as soon as delta = omega(log n). Our construction does not need to know the value of delta in advance and remains fast and effective even when up to a constant fraction of the available memory is corrupted. Our techniques can be immediately extended to implement other data types (e.g., associative containers and priority queues), which can then be used as a building block in the design of other resilient algorithms. For example, we are able to solve the resilient sorting problem in our model using O(n log n) time.
Cite as

Stefano Leucci, Chih-Hung Liu, and Simon Meierhans. Resilient Dictionaries for Randomly Unreliable Memory. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 70:1-70:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{leucci_et_al:LIPIcs.ESA.2019.70,
  author =	{Leucci, Stefano and Liu, Chih-Hung and Meierhans, Simon},
  title =	{{Resilient Dictionaries for Randomly Unreliable Memory}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{70:1--70:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.70},
  URN =		{urn:nbn:de:0030-drops-111911},
  doi =		{10.4230/LIPIcs.ESA.2019.70},
  annote =	{Keywords: resilient dictionary, unreliable memory, faulty RAM}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.58
A Nearly Optimal Algorithm for the Geodesic Voronoi Diagram of Points in a Simple Polygon

Authors: Chih-Hung Liu

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
The geodesic Voronoi diagram of m point sites inside a simple polygon of n vertices is a subdivision of the polygon into m cells, one to each site, such that all points in a cell share the same nearest site under the geodesic distance. The best known lower bound for the construction time is Omega(n+m log m), and a matching upper bound is a long-standing open question. The state-of-the-art construction algorithms achieve O((n+m)log (n+m)) and O(n+m log m log^2n) time, which are optimal for m=Omega(n) and m=O(n/(log^3n)), respectively. In this paper, we give a construction algorithm with O(n+m(log m+log^2 n)) time, and it is nearly optimal in the sense that if a single Voronoi vertex can be computed in O(log n) time, then the construction time will become the optimal O(n+m log m). In other words, we reduce the problem of constructing the diagram in the optimal time to the problem of computing a single Voronoi vertex in O(log n) time.
Cite as

Chih-Hung Liu. A Nearly Optimal Algorithm for the Geodesic Voronoi Diagram of Points in a Simple Polygon. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{liu:LIPIcs.SoCG.2018.58,
  author =	{Liu, Chih-Hung},
  title =	{{A Nearly Optimal Algorithm for the Geodesic Voronoi Diagram of Points in a Simple Polygon}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{58:1--58:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.58},
  URN =		{urn:nbn:de:0030-drops-87717},
  doi =		{10.4230/LIPIcs.SoCG.2018.58},
  annote =	{Keywords: Simple polygons, Voronoi diagrams, Geodesic distance}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.36
Optimal Dislocation with Persistent Errors in Subquadratic Time

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We study the problem of sorting N elements in presence of persistent errors in comparisons: In this classical model, each comparison between two elements is wrong independently with some probability p, but repeating the same comparison gives always the same result. The best known algorithms for this problem have running time O(N^2) and achieve an optimal maximum dislocation of O(log N) for constant error probability. Note that no algorithm can achieve dislocation o(log N), regardless of its running time. In this work we present the first subquadratic time algorithm with optimal maximum dislocation: Our algorithm runs in tilde{O}(N^{3/2}) time and guarantees O(log N) maximum dislocation with high probability. Though the first version of our algorithm is randomized, it can be derandomized by extracting the necessary random bits from the results of the comparisons (errors).
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Optimal Dislocation with Persistent Errors in Subquadratic Time. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{geissmann_et_al:LIPIcs.STACS.2018.36,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Optimal Dislocation with Persistent Errors in Subquadratic Time}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.36},
  URN =		{urn:nbn:de:0030-drops-85266},
  doi =		{10.4230/LIPIcs.STACS.2018.36},
  annote =	{Keywords: sorting, recurrent comparison errors, maximum dislocation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.38
Sorting with Recurrent Comparison Errors

Authors: Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation with high probability, or o(n) total dislocation in expectation, regardless of their running time.
Cite as

Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Sorting with Recurrent Comparison Errors. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 38:1-38:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{geissmann_et_al:LIPIcs.ISAAC.2017.38,
  author =	{Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
  title =	{{Sorting with Recurrent Comparison Errors}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{38:1--38:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.38},
  URN =		{urn:nbn:de:0030-drops-82652},
  doi =		{10.4230/LIPIcs.ISAAC.2017.38},
  annote =	{Keywords: sorting, recurrent comparison error, maximum and total dislocation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.21
An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams

Authors: Cecilia Bohler, Rolf Klein, and Chih-Hung Liu

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
Given a set of n sites in the plane, the order-k Voronoi diagram is a planar subdivision such that all points in a region share the same k nearest sites. The order-k Voronoi diagram arises for the k-nearest-neighbor problem, and there has been a lot of work for point sites in the Euclidean metric. In this paper, we study order-k Voronoi diagrams defined by an abstract bisecting curve system that satisfies several practical axioms, and thus our study covers many concrete order-k Voronoi diagrams. We propose a randomized incremental construction algorithm that runs in O(k(n-k) log^2 n +n log^3 n) steps, where O(k(n-k)) is the number of faces in the worst case. Due to those axioms, this result applies to disjoint line segments in the L_p norm, convex polygons of constant size, points in the Karlsruhe metric, and so on. In fact, this kind of run time with a polylog factor to the number of faces was only achieved for point sites in the L_1 or Euclidean metric before.
Cite as

Cecilia Bohler, Rolf Klein, and Chih-Hung Liu. An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bohler_et_al:LIPIcs.SoCG.2016.21,
  author =	{Bohler, Cecilia and Klein, Rolf and Liu, Chih-Hung},
  title =	{{An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.21},
  URN =		{urn:nbn:de:0030-drops-59135},
  doi =		{10.4230/LIPIcs.SoCG.2016.21},
  annote =	{Keywords: Order-k Voronoi Diagrams, Abstract Voronoi Diagrams, Randomized Geometric Algorithms}
}

Liu, Cong

Document
DOI: 10.4230/LIPIcs.ECRTS.2024.14
GCAPS: GPU Context-Aware Preemptive Priority-Based Scheduling for Real-Time Tasks

Authors: Yidi Wang, Cong Liu, Daniel Wong, and Hyoseung Kim

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Scheduling real-time tasks that utilize GPUs with analyzable guarantees poses a significant challenge due to the intricate interaction between CPU and GPU resources, as well as the complex GPU hardware and software stack. While much research has been conducted in the real-time research community, several limitations persist, including the absence or limited availability of GPU-level preemption, extended blocking times, and/or the need for extensive modifications to program code. In this paper, we propose GCAPS, a GPU Context-Aware Preemptive Scheduling approach for real-time GPU tasks. Our approach exerts control over GPU context scheduling at the device driver level and enables preemption of GPU execution based on task priorities by simply adding one-line macros to GPU segment boundaries. In addition, we provide a comprehensive response time analysis of GPU-using tasks for both our proposed approach as well as the default Nvidia GPU driver scheduling that follows a work-conserving round-robin policy. Through empirical evaluations and case studies, we demonstrate the effectiveness of the proposed approaches in improving taskset schedulability and response time. The results highlight significant improvements over prior work as well as the default scheduling approach, with up to 40% higher schedulability, while also achieving predictable worst-case behavior on Nvidia Jetson embedded platforms.
Cite as

Yidi Wang, Cong Liu, Daniel Wong, and Hyoseung Kim. GCAPS: GPU Context-Aware Preemptive Priority-Based Scheduling for Real-Time Tasks. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wang_et_al:LIPIcs.ECRTS.2024.14,
  author =	{Wang, Yidi and Liu, Cong and Wong, Daniel and Kim, Hyoseung},
  title =	{{GCAPS: GPU Context-Aware Preemptive Priority-Based Scheduling for Real-Time Tasks}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.14},
  URN =		{urn:nbn:de:0030-drops-203170},
  doi =		{10.4230/LIPIcs.ECRTS.2024.14},
  annote =	{Keywords: Real-time systems, GPU scheduling}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2017.15
Optimal Dataflow Scheduling on a Heterogeneous Multiprocessor With Reduced Response Time Bounds

Authors: Zheng Dong, Cong Liu, Alan Gatherer, Lee McFearin, Peter Yan, and James H. Anderson

Published in: LIPIcs, Volume 76, 29th Euromicro Conference on Real-Time Systems (ECRTS 2017)

Abstract
Heterogeneous computing platforms with multiple types of computing resources have been widely used in many industrial systems to process dataflow tasks with pre-defined affinity of tasks to subgroups of resources. For many dataflow workloads with soft real-time requirements, guaranteeing fast and bounded response times is often the objective. This paper presents a new set of analysis techniques showing that a classical real-time scheduler, namely earliest-deadline first (EDF), is able to support dataflow tasks scheduled on such heterogeneous platforms with provably bounded response times while incurring no resource capacity loss, thus proving EDF to be an optimal solution for this scheduling problem. Experiments using synthetic workloads with widely varied parameters also demonstrate that the magnitude of the response time bounds yielded under the proposed analysis is reasonably small under all scenarios. Compared to the state-of-the-art soft real-time analysis techniques, our test yields a 68% reduction on response time bounds on average. This work demonstrates the potential of applying EDF into practical industrial systems containing dataflow-based workloads that desire guaranteed bounded response times.
Cite as

Zheng Dong, Cong Liu, Alan Gatherer, Lee McFearin, Peter Yan, and James H. Anderson. Optimal Dataflow Scheduling on a Heterogeneous Multiprocessor With Reduced Response Time Bounds. In 29th Euromicro Conference on Real-Time Systems (ECRTS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 76, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dong_et_al:LIPIcs.ECRTS.2017.15,
  author =	{Dong, Zheng and Liu, Cong and Gatherer, Alan and McFearin, Lee and Yan, Peter and Anderson, James H.},
  title =	{{Optimal Dataflow Scheduling on a Heterogeneous Multiprocessor With Reduced Response Time Bounds}},
  booktitle =	{29th Euromicro Conference on Real-Time Systems (ECRTS 2017)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-037-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{76},
  editor =	{Bertogna, Marko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2017.15},
  URN =		{urn:nbn:de:0030-drops-71565},
  doi =		{10.4230/LIPIcs.ECRTS.2017.15},
  annote =	{Keywords: Real-time Scheduling, schedulability, heterogeneous multiprocessor}
}

Liu, Chang

Document
DOI: 10.4230/LIPIcs.CP.2023.14
Fast Matrix Multiplication Without Tears: A Constraint Programming Approach

Authors: Arnaud Deza, Chang Liu, Pashootan Vaezipoor, and Elias B. Khalil

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract
It is known that the multiplication of an N × M matrix with an M × P matrix can be performed using fewer multiplications than what the naive NMP approach suggests. The most famous instance of this is Strassen’s algorithm for multiplying 2× 2 matrices in 7 instead of 8 multiplications. This gives rise to the constraint satisfaction problem of fast matrix multiplication, where a set of R < NMP multiplication terms must be chosen and combined such that they satisfy correctness constraints on the output matrix. Despite its highly combinatorial nature, this problem has not been exhaustively examined from that perspective, as evidenced for example by the recent deep reinforcement learning approach of AlphaTensor. In this work, we propose a simple yet novel Constraint Programming approach to find algorithms for fast matrix multiplication or provide proof of infeasibility otherwise. We propose a set of symmetry-breaking constraints and valid inequalities that are particularly helpful in proving infeasibility. On the feasible side, we find that exploiting solver performance variability in conjunction with a sparsity-based problem decomposition enables finding solutions for larger (feasible) instances of fast matrix multiplication. Our experimental results using CP Optimizer demonstrate that we can find fast matrix multiplication algorithms for matrices up to 3× 3 with R = 23 in a short amount of time.
Cite as

Arnaud Deza, Chang Liu, Pashootan Vaezipoor, and Elias B. Khalil. Fast Matrix Multiplication Without Tears: A Constraint Programming Approach. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{deza_et_al:LIPIcs.CP.2023.14,
  author =	{Deza, Arnaud and Liu, Chang and Vaezipoor, Pashootan and Khalil, Elias B.},
  title =	{{Fast Matrix Multiplication Without Tears: A Constraint Programming Approach}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.14},
  URN =		{urn:nbn:de:0030-drops-190518},
  doi =		{10.4230/LIPIcs.CP.2023.14},
  annote =	{Keywords: fast matrix multiplication, computer-assisted proofs, constraint programming, constraint satisfaction problem}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.9
On-Line Pattern Matching on Similar Texts

Authors: Roberto Grossi, Costas S. Iliopoulos, Chang Liu, Nadia Pisanti, Solon P. Pissis, Ahmad Retha, Giovanna Rosone, Fatima Vayani, and Luca Versari

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract
Pattern matching on a set of similar texts has received much attention, especially recently, mainly due to its application in cataloguing human genetic variation. In particular, many different algorithms have been proposed for the off-line version of this problem; that is, constructing a compressed index for a set of similar texts in order to answer pattern matching queries efficiently. However, the on-line, more fundamental, version of this problem is a rather undeveloped topic. Solutions to the on-line version can be beneficial for a number of reasons; for instance, efficient on-line solutions can be used in combination with partial indexes as practical trade-offs. We make here an attempt to close this gap via proposing two efficient algorithms for this problem. Notably, one of the algorithms requires time linear in the size of the texts' representation, for short patterns. Furthermore, experimental results confirm our theoretical findings in practical terms.
Cite as

Roberto Grossi, Costas S. Iliopoulos, Chang Liu, Nadia Pisanti, Solon P. Pissis, Ahmad Retha, Giovanna Rosone, Fatima Vayani, and Luca Versari. On-Line Pattern Matching on Similar Texts. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{grossi_et_al:LIPIcs.CPM.2017.9,
  author =	{Grossi, Roberto and Iliopoulos, Costas S. and Liu, Chang and Pisanti, Nadia and Pissis, Solon P. and Retha, Ahmad and Rosone, Giovanna and Vayani, Fatima and Versari, Luca},
  title =	{{On-Line Pattern Matching on Similar Texts}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.9},
  URN =		{urn:nbn:de:0030-drops-73379},
  doi =		{10.4230/LIPIcs.CPM.2017.9},
  annote =	{Keywords: string algorithms, pattern matching, degenerate strings, elastic-degenerate strings, on-line algorithms}
}
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