12 Search Results for "Zhang, Simon"


Document
Position
Large Language Models and Knowledge Graphs: Opportunities and Challenges

Authors: Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1


Abstract
Large Language Models (LLMs) have taken Knowledge Representation - and the world - by storm. This inflection point marks a shift from explicit knowledge representation to a renewed focus on the hybrid representation of both explicit knowledge and parametric knowledge. In this position paper, we will discuss some of the common debate points within the community on LLMs (parametric knowledge) and Knowledge Graphs (explicit knowledge) and speculate on opportunities and visions that the renewed focus brings, as well as related research topics and challenges.

Cite as

Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux. Large Language Models and Knowledge Graphs: Opportunities and Challenges. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 2:1-2:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@Article{pan_et_al:TGDK.1.1.2,
  author =	{Pan, Jeff Z. and Razniewski, Simon and Kalo, Jan-Christoph and Singhania, Sneha and Chen, Jiaoyan and Dietze, Stefan and Jabeen, Hajira and Omeliyanenko, Janna and Zhang, Wen and Lissandrini, Matteo and Biswas, Russa and de Melo, Gerard and Bonifati, Angela and Vakaj, Edlira and Dragoni, Mauro and Graux, Damien},
  title =	{{Large Language Models and Knowledge Graphs: Opportunities and Challenges}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:38},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.2},
  URN =		{urn:nbn:de:0030-drops-194766},
  doi =		{10.4230/TGDK.1.1.2},
  annote =	{Keywords: Large Language Models, Pre-trained Language Models, Knowledge Graphs, Ontology, Retrieval Augmented Language Models}
}
Document
Practical Large-Scale Proof-Of-Stake Asynchronous Total-Order Broadcast

Authors: Orestis Alpos, Christian Cachin, Simon Holmgaard Kamp, and Jesper Buus Nielsen

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)


Abstract
We present simple and practical protocols for generating randomness as used by asynchronous total-order broadcast. The protocols are secure in a proof-of-stake setting with dynamically changing stake. They can be plugged into existing protocols for asynchronous total-order broadcast and will turn these into asynchronous total-order broadcast with dynamic stake. Our contribution relies on two important techniques. The paper "Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement using Cryptography" [Cachin, Kursawe, and Shoup, PODC 2000] has influenced the design of practical total-order broadcast through its use of threshold cryptography. However, it needs a setup protocol to be efficient. In a proof-of-stake setting with dynamic stake this setup would have to be continually recomputed, making the protocol impractical. The work "Asynchronous Byzantine Agreement with Subquadratic Communication" [Blum, Katz, Liu-Zhang, and Loss, TCC 2020] showed how to use an initial setup for broadcast to asymptotically efficiently generate sub-sequent setups. The protocol, however, resorted to fully homomorphic encryption and was therefore not practically efficient. We adopt their approach to the proof-of-stake setting with dynamic stake, apply it to the Constantinople paper, and remove the need for fully homomorphic encryption. This results in simple and practical proof-of-stake protocols.

Cite as

Orestis Alpos, Christian Cachin, Simon Holmgaard Kamp, and Jesper Buus Nielsen. Practical Large-Scale Proof-Of-Stake Asynchronous Total-Order Broadcast. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{alpos_et_al:LIPIcs.AFT.2023.31,
  author =	{Alpos, Orestis and Cachin, Christian and Kamp, Simon Holmgaard and Nielsen, Jesper Buus},
  title =	{{Practical Large-Scale Proof-Of-Stake Asynchronous Total-Order Broadcast}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{31:1--31:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.31},
  URN =		{urn:nbn:de:0030-drops-192203},
  doi =		{10.4230/LIPIcs.AFT.2023.31},
  annote =	{Keywords: Total-Order Broadcast, Atomic Broadcast, Proof of Stake, Random Beacon}
}
Document
Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings

Authors: Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, [Christoph Dürr et al., 2020] has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a (4+ε)-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a (2+ε)-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time 𝒪(poly(n/ε)). Lastly, we show that our results are essentially optimal by providing matching lower bounds.

Cite as

Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang. Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{damerius_et_al:LIPIcs.ESA.2023.38,
  author =	{Damerius, Christoph and Kling, Peter and Li, Minming and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.38},
  URN =		{urn:nbn:de:0030-drops-186915},
  doi =		{10.4230/LIPIcs.ESA.2023.38},
  annote =	{Keywords: scheduling, total completion time, makespan, LP rounding, competitive analysis, approximation algorithm, NP hardness, PTAS}
}
Document
Efficient 1-Laplacian Solvers for Well-Shaped Simplicial Complexes: Beyond Betti Numbers and Collapsing Sequences

Authors: Ming Ding and Peng Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We present efficient algorithms for solving systems of linear equations in 1-Laplacians of well-shaped simplicial complexes. 1-Laplacians, or higher-dimensional Laplacians, generalize graph Laplacians to higher-dimensional simplicial complexes and play a key role in computational topology and topological data analysis. Previously, nearly-linear time solvers were developed for simplicial complexes with known collapsing sequences and bounded Betti numbers, such as those triangulating a three-ball in ℝ³ (Cohen, Fasy, Miller, Nayyeri, Peng, and Walkington [SODA'2014], Black, Maxwell, Nayyeri, and Winkelman [SODA'2022], Black and Nayyeri [ICALP'2022]). Furthermore, Nested Dissection provides quadratic time solvers for more general systems with nonzero structures representing well-shaped simplicial complexes embedded in ℝ³. We generalize the specialized solvers for 1-Laplacians to simplicial complexes with additional geometric structures but without collapsing sequences and bounded Betti numbers, and we improve the runtime of Nested Dissection. We focus on simplicial complexes that meet two conditions: (1) each individual simplex has a bounded aspect ratio, and (2) they can be divided into "disjoint" and balanced regions with well-shaped interiors and boundaries. Our solvers draw inspiration from the Incomplete Nested Dissection for stiffness matrices of well-shaped trusses (Kyng, Peng, Schwieterman, and Zhang [STOC'2018]).

Cite as

Ming Ding and Peng Zhang. Efficient 1-Laplacian Solvers for Well-Shaped Simplicial Complexes: Beyond Betti Numbers and Collapsing Sequences. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{ding_et_al:LIPIcs.ESA.2023.41,
  author =	{Ding, Ming and Zhang, Peng},
  title =	{{Efficient 1-Laplacian Solvers for Well-Shaped Simplicial Complexes: Beyond Betti Numbers and Collapsing Sequences}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.41},
  URN =		{urn:nbn:de:0030-drops-186947},
  doi =		{10.4230/LIPIcs.ESA.2023.41},
  annote =	{Keywords: 1-Laplacian Solvers, Simplicial Complexes, Incomplete Nested Dissection}
}
Document
On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching

Authors: Jingxun Liang, Zhihao Gavin Tang, Yixuan Even Xu, Yuhao Zhang, and Renfei Zhou

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Ranking and Balance are arguably the two most important algorithms in the online matching literature. They achieve the same optimal competitive ratio of 1-1/e for the integral version and fractional version of online bipartite matching by Karp, Vazirani, and Vazirani (STOC 1990) respectively. The two algorithms have been generalized to weighted online bipartite matching problems, including vertex-weighted online bipartite matching and AdWords, by utilizing a perturbation function. The canonical choice of the perturbation function is f(x) = 1-e^{x-1} as it leads to the optimal competitive ratio of 1-1/e in both settings. We advance the understanding of the weighted generalizations of Ranking and Balance in this paper, with a focus on studying the effect of different perturbation functions. First, we prove that the canonical perturbation function is the unique optimal perturbation function for vertex-weighted online bipartite matching. In stark contrast, all perturbation functions achieve the optimal competitive ratio of 1-1/e in the unweighted setting. Second, we prove that the generalization of Ranking to AdWords with unknown budgets using the canonical perturbation function is at most 0.624 competitive, refuting a conjecture of Vazirani (2021). More generally, as an application of the first result, we prove that no perturbation function leads to the prominent competitive ratio of 1-1/e by establishing an upper bound of 1-1/e-0.0003. Finally, we propose the online budget-additive welfare maximization problem that is intermediate between AdWords and AdWords with unknown budgets, and we design an optimal 1-1/e competitive algorithm by generalizing Balance.

Cite as

Jingxun Liang, Zhihao Gavin Tang, Yixuan Even Xu, Yuhao Zhang, and Renfei Zhou. On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{liang_et_al:LIPIcs.ESA.2023.80,
  author =	{Liang, Jingxun and Tang, Zhihao Gavin and Xu, Yixuan Even and Zhang, Yuhao and Zhou, Renfei},
  title =	{{On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{80:1--80:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.80},
  URN =		{urn:nbn:de:0030-drops-187334},
  doi =		{10.4230/LIPIcs.ESA.2023.80},
  annote =	{Keywords: Online Matching, AdWords, Ranking, Water-Filling}
}
Document
Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs

Authors: Enze Sun, Zonghan Yang, and Yuhao Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We consider the Online Rent Minimization problem, where online jobs with release times, deadlines, and processing times must be scheduled on machines that can be rented for a fixed length period of T. The objective is to minimize the number of machine rents. This problem generalizes the Online Machine Minimization problem where machines can be rented for an infinite period, and both problems have an asymptotically optimal competitive ratio of O(log(p_max/p_min)) for general processing times, where p_max and p_min are the maximum and minimum processing times respectively. However, for small values of p_max/p_min, a better competitive ratio can be achieved by assuming unit-size jobs. Under this assumption, Devanur et al. (2014) gave an optimal e-competitive algorithm for Online Machine Minimization, and Chen and Zhang (2022) gave a (3e+7) ≈ 15.16-competitive algorithm for Online Rent Minimization. In this paper, we significantly improve the competitive ratio of the Online Rent Minimization problem under unit size to 6, by using a clean oracle-based online algorithm framework.

Cite as

Enze Sun, Zonghan Yang, and Yuhao Zhang. Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{sun_et_al:LIPIcs.ESA.2023.97,
  author =	{Sun, Enze and Yang, Zonghan and Zhang, Yuhao},
  title =	{{Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{97:1--97:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.97},
  URN =		{urn:nbn:de:0030-drops-187500},
  doi =		{10.4230/LIPIcs.ESA.2023.97},
  annote =	{Keywords: Online Algorithm, Scheduling, Machine Minimization, Rent Minimization}
}
Document
Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

Authors: Xiaoming Sun, Jialin Zhang, and Zhijie Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP). In SMKP, the profits of each subset of elements are specified by a monotone submodular function. The goal is to find a feasible packing of elements over multiple bins (knapsacks) to maximize the profit. Recently, Fairstein et al. [ESA20] proposed a nearly optimal (1-e^{-1}-ε)-approximation algorithm for SMKP. Their algorithm is obtained by combining configuration LP, a grouping technique for bin packing, and the continuous greedy algorithm for submodular maximization. As a result, the algorithm is somewhat sophisticated and inherently randomized. In this paper, we present an arguably simple deterministic combinatorial algorithm for SMKP, which achieves a (1-e^{-1}-ε)-approximation ratio. Our algorithm is based on very different ideas compared with Fairstein et al. [ESA20].

Cite as

Xiaoming Sun, Jialin Zhang, and Zhijie Zhang. Simple Deterministic Approximation for Submodular Multiple Knapsack Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{sun_et_al:LIPIcs.ESA.2023.98,
  author =	{Sun, Xiaoming and Zhang, Jialin and Zhang, Zhijie},
  title =	{{Simple Deterministic Approximation for Submodular Multiple Knapsack Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{98:1--98:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.98},
  URN =		{urn:nbn:de:0030-drops-187517},
  doi =		{10.4230/LIPIcs.ESA.2023.98},
  annote =	{Keywords: Submodular maximization, knapsack problem, deterministic algorithm}
}
Document
Diameter Versus Certificate Complexity of Boolean Functions

Authors: Siddhesh Chaubal and Anna Gál

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
In this paper, we introduce a measure of Boolean functions we call diameter, that captures the relationship between certificate complexity and several other measures of Boolean functions. Our measure can be viewed as a variation on alternating number, but while alternating number can be exponentially larger than certificate complexity, we show that diameter is always upper bounded by certificate complexity. We argue that estimating diameter may help to get improved bounds on certificate complexity in terms of sensitivity, and other measures. Previous results due to Lin and Zhang [Krishnamoorthy Dinesh and Jayalal Sarma, 2018] imply that s(f) ≥ Ω(n^{1/3}) for transitive functions with constant alternating number. We improve and extend this bound and prove that s(f) ≥ √n for transitive functions with constant alternating number, as well as for transitive functions with constant diameter. {We also show that bs(f) ≥ Ω(n^{3/7}) for transitive functions under the weaker condition that the "minimum" diameter is constant.} Furthermore, we prove that the log-rank conjecture holds for functions of the form f(x ⊕ y) for functions f with diameter bounded above by a polynomial of the logarithm of the Fourier sparsity of the function f.

Cite as

Siddhesh Chaubal and Anna Gál. Diameter Versus Certificate Complexity of Boolean Functions. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{chaubal_et_al:LIPIcs.MFCS.2021.31,
  author =	{Chaubal, Siddhesh and G\'{a}l, Anna},
  title =	{{Diameter Versus Certificate Complexity of Boolean Functions}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{31:1--31:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.31},
  URN =		{urn:nbn:de:0030-drops-144713},
  doi =		{10.4230/LIPIcs.MFCS.2021.31},
  annote =	{Keywords: Sensitivity Conjecture, Boolean Functions, Certificate Complexity, Block Sensitivity, Log-rank Conjecture, Alternating Number}
}
Document
Invited Talk
Convex Optimization and Dynamic Data Structure (Invited Talk)

Authors: Yin Tat Lee

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
In the last three years, there are many breakthroughs in optimization such as nearly quadratic time algorithms for bipartite matching, linear programming algorithms that are as fast as Ax = b. All of these algorithms are based on a careful combination of optimization techniques and dynamic data structures. In this talk, we will explain the framework underlying all the recent breakthroughs. Joint work with Jan van den Brand, Michael B. Cohen, Sally Dong, Haotian Jiang, Tarun Kathuria, Danupon Nanongkai, Swati Padmanabhan, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang, Sam Chiu-wai Wong, Guanghao Ye, Qiuyi Zhang.

Cite as

Yin Tat Lee. Convex Optimization and Dynamic Data Structure (Invited Talk). In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{lee:LIPIcs.FSTTCS.2020.3,
  author =	{Lee, Yin Tat},
  title =	{{Convex Optimization and Dynamic Data Structure}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-132440},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.3},
  annote =	{Keywords: Convex Optimization, Dynamic Data Structure}
}
Document
On Parity Decision Trees for Fourier-Sparse Boolean Functions

Authors: Nikhil S. Mande and Swagato Sanyal

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows. Let f : 𝔽₂ⁿ → {-1, 1} be a Boolean function with Fourier support 𝒮 and Fourier sparsity k. - We prove via the probabilistic method that there exists a parity decision tree of depth O(√k) that computes f. This matches the best known upper bound on the parity decision tree complexity of Boolean functions (Tsang, Wong, Xie, and Zhang, FOCS 2013). Moreover, while previous constructions (Tsang et al., FOCS 2013, Shpilka, Tal, and Volk, Comput. Complex. 2017) build the trees by carefully choosing the parities to be queried in each step, our proof shows that a naive sampling of the parities suffices. - We generalize the above result by showing that if the Fourier spectra of Boolean functions satisfy a natural "folding property", then the above proof can be adapted to establish existence of a tree of complexity polynomially smaller than O(√ k). More concretely, the folding property we consider is that for most distinct γ, δ in 𝒮, there are at least a polynomial (in k) number of pairs (α, β) of parities in 𝒮 such that α+β = γ+δ. We make a conjecture in this regard which, if true, implies that the communication complexity of an XOR function is bounded above by the fourth root of the rank of its communication matrix, improving upon the previously known upper bound of square root of rank (Tsang et al., FOCS 2013, Lovett, J. ACM. 2016). - Motivated by the above, we present some structural results about the Fourier spectra of Boolean functions. It can be shown by elementary techniques that for any Boolean function f and all (α, β) in binom(𝒮,2), there exists another pair (γ, δ) in binom(𝒮,2) such that α + β = γ + δ. One can view this as a "trivial" folding property that all Boolean functions satisfy. Prior to our work, it was conceivable that for all (α, β) ∈ binom(𝒮,2), there exists exactly one other pair (γ, δ) ∈ binom(𝒮,2) with α + β = γ + δ. We show, among other results, that there must exist several γ ∈ 𝔽₂ⁿ such that there are at least three pairs of parities (α₁, α₂) ∈ binom(𝒮,2) with α₁+α₂ = γ. This, in particular, rules out the possibility stated earlier.

Cite as

Nikhil S. Mande and Swagato Sanyal. On Parity Decision Trees for Fourier-Sparse Boolean Functions. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{mande_et_al:LIPIcs.FSTTCS.2020.29,
  author =	{Mande, Nikhil S. and Sanyal, Swagato},
  title =	{{On Parity Decision Trees for Fourier-Sparse Boolean Functions}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.29},
  URN =		{urn:nbn:de:0030-drops-132703},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.29},
  annote =	{Keywords: Parity decision trees, log-rank conjecture, analysis of Boolean functions, communication complexity}
}
Document
GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes

Authors: Simon Zhang, Mengbai Xiao, and Hao Wang

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
The computation of Vietoris-Rips persistence barcodes is both execution-intensive and memory-intensive. In this paper, we study the computational structure of Vietoris-Rips persistence barcodes, and identify several unique mathematical properties and algorithmic opportunities with connections to the GPU. Mathematically and empirically, we look into the properties of apparent pairs, which are independently identifiable persistence pairs comprising up to 99% of persistence pairs. We give theoretical upper and lower bounds of the apparent pair rate and model the average case. We also design massively parallel algorithms to take advantage of the very large number of simplices that can be processed independently of each other. Having identified these opportunities, we develop a GPU-accelerated software for computing Vietoris-Rips persistence barcodes, called Ripser++. The software achieves up to 30x speedup over the total execution time of the original Ripser and also reduces CPU-memory usage by up to 2.0x. We believe our GPU-acceleration based efforts open a new chapter for the advancement of topological data analysis in the post-Moore’s Law era.

Cite as

Simon Zhang, Mengbai Xiao, and Hao Wang. GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{zhang_et_al:LIPIcs.SoCG.2020.70,
  author =	{Zhang, Simon and Xiao, Mengbai and Wang, Hao},
  title =	{{GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{70:1--70:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.70},
  URN =		{urn:nbn:de:0030-drops-122287},
  doi =		{10.4230/LIPIcs.SoCG.2020.70},
  annote =	{Keywords: Parallel Algorithms, Topological Data Analysis, Vietoris-Rips, Persistent Homology, Apparent Pairs, High Performance Computing, GPU, Random Graphs}
}
Document
The Weighted k-Center Problem in Trees for Fixed k

Authors: Binay Bhattacharya, Sandip Das, and Subhadeep Ranjan Dev

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


Abstract
We present a linear time algorithm for the weighted k-center problem on trees for fixed k. This partially settles the long-standing question about the lower bound on the time complexity of the problem. The current time complexity of the best-known algorithm for the problem with k as part of the input is O(n log n) by Wang et al. [Haitao Wang and Jingru Zhang, 2018]. Whether an O(n) time algorithm exists for arbitrary k is still open.

Cite as

Binay Bhattacharya, Sandip Das, and Subhadeep Ranjan Dev. The Weighted k-Center Problem in Trees for Fixed k. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 27:1-27:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bhattacharya_et_al:LIPIcs.ISAAC.2019.27,
  author =	{Bhattacharya, Binay and Das, Sandip and Dev, Subhadeep Ranjan},
  title =	{{The Weighted k-Center Problem in Trees for Fixed k}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{27:1--27:11},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.27},
  URN =		{urn:nbn:de:0030-drops-115238},
  doi =		{10.4230/LIPIcs.ISAAC.2019.27},
  annote =	{Keywords: facility location, prune and search, parametric search, k-center problem, conditional k-center problem, trees}
}
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