11 Search Results for "Lin, Ting-Chun"

Document
DOI: 10.4230/LIPIcs.CCC.2024.7
Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.
Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.6
Faster Treewidth-Based Approximations for Wiener Index

Authors: Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The Wiener index of a graph G is the sum of distances between all pairs of its vertices. It is a widely-used graph property in chemistry, initially introduced to examine the link between boiling points and structural properties of alkanes, which later found notable applications in drug design. Thus, computing or approximating the Wiener index of molecular graphs, i.e. graphs in which every vertex models an atom of a molecule and every edge models a bond, is of significant interest to the computational chemistry community. In this work, we build upon the observation that molecular graphs are sparse and tree-like and focus on developing efficient algorithms parameterized by treewidth to approximate the Wiener index. We present a new randomized approximation algorithm using a combination of tree decompositions and centroid decompositions. Our algorithm approximates the Wiener index within any desired multiplicative factor (1 ± ε) in time O(n ⋅ log n ⋅ k³ + √n ⋅ k/ε²), where n is the number of vertices of the graph and k is the treewidth. This time bound is almost-linear in n. Finally, we provide experimental results over standard benchmark molecules from PubChem and the Protein Data Bank, showcasing the applicability and scalability of our approach on real-world chemical graphs and comparing it with previous methods.
Cite as

Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani. Faster Treewidth-Based Approximations for Wiener Index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{conrado_et_al:LIPIcs.SEA.2024.6,
  author =	{Conrado, Giovanna Kobus and Goharshady, Amir Kafshdar and Hudec, Pavel and Li, Pingjiang and Motwani, Harshit Jitendra},
  title =	{{Faster Treewidth-Based Approximations for Wiener Index}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.6},
  URN =		{urn:nbn:de:0030-drops-203718},
  doi =		{10.4230/LIPIcs.SEA.2024.6},
  annote =	{Keywords: Computational Chemistry, Treewidth, Wiener Index}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.9
Top- k Frequent Patterns in Streams and Parameterized-Space LZ Compression

Authors: Patrick Dinklage, Johnnes Fischer, and Nicola Prezza

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
We present novel online approximations of the Lempel-Ziv 77 (LZ77) and Lempel-Ziv 78 (LZ78) compression schemes [Lempel & Ziv, 1977/1978] with parameterizable space usage based on estimating which k patterns occur the most frequently in the streamed input for parameter k. This new approach overcomes the issue of finding only local repetitions, which is a natural limitation of algorithms that compress using a sliding window or by partitioning the input into blocks. For this, we introduce the top-k trie, a summary for maintaining online the top-k frequent consecutive patterns in a stream of characters based on a combination of the Lempel-Ziv 78 compression scheme and the Misra-Gries algorithm for frequent item estimation in streams. Using straightforward encoding, our implementations yield compression ratios (output over input size) competitive with established general-purpose LZ-based compression utilities such as gzip or xz.
Cite as

Patrick Dinklage, Johnnes Fischer, and Nicola Prezza. Top- k Frequent Patterns in Streams and Parameterized-Space LZ Compression. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dinklage_et_al:LIPIcs.SEA.2024.9,
  author =	{Dinklage, Patrick and Fischer, Johnnes and Prezza, Nicola},
  title =	{{Top- k Frequent Patterns in Streams and Parameterized-Space LZ Compression}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.9},
  URN =		{urn:nbn:de:0030-drops-203748},
  doi =		{10.4230/LIPIcs.SEA.2024.9},
  annote =	{Keywords: compression, streaming, heavy hitters, algorithm engineering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.17
Vital Edges for (s,t)-Mincut: Efficient Algorithms, Compact Structures, & Optimal Sensitivity Oracles

Authors: Surender Baswana and Koustav Bhanja

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Let G be a directed weighted graph on n vertices and m edges with designated source and sink vertices s and t. An edge in G is vital if its removal reduces the capacity of (s,t)-mincut. Since the seminal work of Ford and Fulkerson [CJM 1956], a long line of work has been done on computing the most vital edge and all vital edges of G. However, even after 60 years, the existing results are for either undirected or unweighted graphs. We present the following result for directed weighted graphs that also solves an open problem by Ausiello, Franciosa, Lari, and Ribichini [NETWORKS 2019]. 1. Algorithmic Results: There is an algorithm that computes all vital edges as well as the most vital edge of G using {O}(n) maximum (s,t)-flow computations. Vital edges play a crucial role in the design of sensitivity oracle for (s,t)-mincut - a compact data structure for reporting (s,t)-mincut after insertion/failure of any edge. For directed graphs, the only existing sensitivity oracle is for unweighted graphs by Picard and Queyranne [MPS 1982]. We present the first and optimal sensitivity oracle for directed weighted graphs as follows. 2. Sensitivity Oracles: a) There is an optimal O(n²) space data structure that can report an (s,t)-mincut C in O(|C|) time after the failure/insertion of any edge. b) There is an O(n) space data structure that can report the capacity of (s,t)-mincut after failure or insertion of any edge e in O(1) time if the capacity of edge e is known. A mincut for a vital edge e is an (s,t)-cut of the least capacity in which edge e is outgoing. For unweighted graphs, in a classical work, Picard and Queyranne [MPS 1982] designed an O(m) space directed acyclic graph (DAG) that stores and characterizes all mincuts for all vital edges. Conversely, there is a set containing at most n-1 (s,t)-cuts such that at least one mincut for every vital edge belongs to the set. We generalize these results for directed weighted graphs as follows. 3. Structural & Combinatorial Results: a) There is a set M containing at most n-1 (s,t)-cuts such that at least one mincut for every vital edge belongs to the set. This bound is tight as well. We also show that set M can be computed using O(n) maximum (s,t)-flow computations. b) We design two compact structures for storing and characterizing all mincuts for all vital edges - (i) an O(m) space DAG for partial and (ii) an O(mn) space structure for complete characterization. To arrive at our results, we develop new techniques, especially a generalization of maxflow-mincut Theorem by Ford and Fulkerson [CJM 1956], which might be of independent interest.
Cite as

Surender Baswana and Koustav Bhanja. Vital Edges for (s,t)-Mincut: Efficient Algorithms, Compact Structures, & Optimal Sensitivity Oracles. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baswana_et_al:LIPIcs.ICALP.2024.17,
  author =	{Baswana, Surender and Bhanja, Koustav},
  title =	{{Vital Edges for (s,t)-Mincut: Efficient Algorithms, Compact Structures, \& Optimal Sensitivity Oracles}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.17},
  URN =		{urn:nbn:de:0030-drops-201601},
  doi =		{10.4230/LIPIcs.ICALP.2024.17},
  annote =	{Keywords: maxflow, vital edges, graph algorithms, structures, st-cuts, sensitivity oracle}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.18
It’s Hard to HAC Average Linkage!

Authors: MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Average linkage Hierarchical Agglomerative Clustering (HAC) is an extensively studied and applied method for hierarchical clustering. Recent applications to massive datasets have driven significant interest in near-linear-time and efficient parallel algorithms for average linkage HAC. We provide hardness results that rule out such algorithms. On the sequential side, we establish a runtime lower bound of n^{3/2-ε} on n node graphs for sequential combinatorial algorithms under standard fine-grained complexity assumptions. This essentially matches the best-known running time for average linkage HAC. On the parallel side, we prove that average linkage HAC likely cannot be parallelized even on simple graphs by showing that it is CC-hard on trees of diameter 4. On the possibility side, we demonstrate that average linkage HAC can be efficiently parallelized (i.e., it is in NC) on paths and can be solved in near-linear time when the height of the output cluster hierarchy is small.
Cite as

MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki. It’s Hard to HAC Average Linkage!. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bateni_et_al:LIPIcs.ICALP.2024.18,
  author =	{Bateni, MohammadHossein and Dhulipala, Laxman and Gowda, Kishen N. and Hershkowitz, D. Ellis and Jayaram, Rajesh and {\L}\k{a}cki, Jakub},
  title =	{{It’s Hard to HAC Average Linkage!}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.18},
  URN =		{urn:nbn:de:0030-drops-201613},
  doi =		{10.4230/LIPIcs.ICALP.2024.18},
  annote =	{Keywords: Clustering, Hierarchical Graph Clustering, HAC, Fine-Grained Complexity, Parallel Algorithms, CC}
}
Document
Survey
DOI: 10.4230/TGDK.2.1.1
Towards Representing Processes and Reasoning with Process Descriptions on the Web

Authors: Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
We work towards a vocabulary to represent processes and temporal logic specifications as graph-structured data. Different fields use incompatible terminologies for describing essentially the same process-related concepts. In addition, processes can be represented from different perspectives and levels of abstraction: both state-centric and event-centric perspectives offer distinct insights into the underlying processes. In this work, we strive to unify the representation of processes and related concepts by leveraging the power of knowledge graphs. We survey approaches to representing processes and reasoning with process descriptions from different fields and provide a selection of scenarios to help inform the scope of a unified representation of processes. We focus on processes that can be executed and observed via web interfaces. We propose to provide a representation designed to combine state-centric and event-centric perspectives while incorporating temporal querying and reasoning capabilities on temporal logic specifications. A standardised vocabulary and representation for processes and temporal specifications would contribute towards bridging the gap between the terminologies from different fields and fostering the broader application of methods involving temporal logics, such as formal verification and program synthesis.
Cite as

Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese. Towards Representing Processes and Reasoning with Process Descriptions on the Web. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 1:1-1:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{harth_et_al:TGDK.2.1.1,
  author =	{Harth, Andreas and K\"{a}fer, Tobias and Rula, Anisa and Calbimonte, Jean-Paul and Kamburjan, Eduard and Giese, Martin},
  title =	{{Towards Representing Processes and Reasoning with Process Descriptions on the Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:32},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.1},
  URN =		{urn:nbn:de:0030-drops-198583},
  doi =		{10.4230/TGDK.2.1.1},
  annote =	{Keywords: Process modelling, Process ontology, Temporal logic, Web services}
}
Document
Position
DOI: 10.4230/TGDK.2.1.5
Standardizing Knowledge Engineering Practices with a Reference Architecture

Authors: Bradley P. Allen and Filip Ilievski

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Knowledge engineering is the process of creating and maintaining knowledge-producing systems. Throughout the history of computer science and AI, knowledge engineering workflows have been widely used given the importance of high-quality knowledge for reliable intelligent agents. Meanwhile, the scope of knowledge engineering, as apparent from its target tasks and use cases, has been shifting, together with its paradigms such as expert systems, semantic web, and language modeling. The intended use cases and supported user requirements between these paradigms have not been analyzed globally, as new paradigms often satisfy prior pain points while possibly introducing new ones. The recent abstraction of systemic patterns into a boxology provides an opening for aligning the requirements and use cases of knowledge engineering with the systems, components, and software that can satisfy them best, however, this direction has not been explored to date. This paper proposes a vision of harmonizing the best practices in the field of knowledge engineering by leveraging the software engineering methodology of creating reference architectures. We describe how a reference architecture can be iteratively designed and implemented to associate user needs with recurring systemic patterns, building on top of existing knowledge engineering workflows and boxologies. We provide a six-step roadmap that can enable the development of such an architecture, consisting of scope definition, selection of information sources, architectural analysis, synthesis of an architecture based on the information source analysis, evaluation through instantiation, and, ultimately, instantiation into a concrete software architecture. We provide an initial design and outcome of the definition of architectural scope, selection of information sources, and analysis. As the remaining steps of design, evaluation, and instantiation of the architecture are largely use-case specific, we provide a detailed description of their procedures and point to relevant examples. We expect that following through on this vision will lead to well-grounded reference architectures for knowledge engineering, will advance the ongoing initiatives of organizing the neurosymbolic knowledge engineering space, and will build new links to the software architectures and data science communities.
Cite as

Bradley P. Allen and Filip Ilievski. Standardizing Knowledge Engineering Practices with a Reference Architecture. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{allen_et_al:TGDK.2.1.5,
  author =	{Allen, Bradley P. and Ilievski, Filip},
  title =	{{Standardizing Knowledge Engineering Practices with a Reference Architecture}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:23},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.5},
  URN =		{urn:nbn:de:0030-drops-198623},
  doi =		{10.4230/TGDK.2.1.5},
  annote =	{Keywords: knowledge engineering, knowledge graphs, quality attributes, software architectures, sociotechnical systems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.6
Pseudorandom Strings from Pseudorandom Quantum States

Authors: Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states that are computationally indistinguishable from Haar random states. PRSGs have found applications in quantum gravity, quantum machine learning, quantum complexity theory, and quantum cryptography. Pseudorandom generators, on the other hand, a pseudorandomness notion in the classical world, is ubiquitous to theoretical computer science. While some separation results were known between PRSGs, for some parameter regimes, and PRGs, their relationship has not been completely understood. In this work, we show that a natural variant of pseudorandom generators called quantum pseudorandom generators (QPRGs) can be based on the existence of logarithmic output length PRSGs. Our result along with the previous separations gives a better picture regarding the relationship between the two notions. We also study the relationship between other notions, namely, pseudorandom function-like state generators and pseudorandom functions. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.
Cite as

Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen. Pseudorandom Strings from Pseudorandom Quantum States. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ananth_et_al:LIPIcs.ITCS.2024.6,
  author =	{Ananth, Prabhanjan and Lin, Yao-Ting and Yuen, Henry},
  title =	{{Pseudorandom Strings from Pseudorandom Quantum States}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.6},
  URN =		{urn:nbn:de:0030-drops-195348},
  doi =		{10.4230/LIPIcs.ITCS.2024.6},
  annote =	{Keywords: Quantum Cryptography}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.33
On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation

Authors: Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time T for the simulation greatly affect algorithm runtime as expected. While there are some specific types of Hamiltonians that can be fast-forwarded, i.e., simulated within time o(T), for some large classes of Hamiltonians (e.g., all local/sparse Hamiltonians), existing simulation algorithms require running time at least linear in the evolution time T. On the other hand, while there exist lower bounds of Ω(T) circuit size for some large classes of Hamiltonian, these lower bounds do not rule out the possibilities of Hamiltonian simulation with large but "low-depth" circuits by running things in parallel. As a result, physical systems with system size scaling with T can potentially do a fast-forwarding simulation. Therefore, it is intriguing whether we can achieve fast Hamiltonian simulation with the power of parallelism. In this work, we give a negative result for the above open problem in various settings. In the oracle model, we prove that there are time-independent sparse Hamiltonians that cannot be simulated via an oracle circuit of depth o(T). In the plain model, relying on the random oracle heuristic, we show that there exist time-independent local Hamiltonians and time-dependent geometrically local Hamiltonians on n qubits that cannot be simulated via an oracle circuit of depth o(T/n^c), where the Hamiltonians act on n qubits, and c is a constant. Lastly, we generalize the above results and show that any simulators that are geometrically local Hamiltonians cannot do the simulation much faster than parallel quantum algorithms.
Cite as

Nai-Hui Chia, Kai-Min Chung, Yao-Ching Hsieh, Han-Hsuan Lin, Yao-Ting Lin, and Yu-Ching Shen. On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 33:1-33:45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chia_et_al:LIPIcs.CCC.2023.33,
  author =	{Chia, Nai-Hui and Chung, Kai-Min and Hsieh, Yao-Ching and Lin, Han-Hsuan and Lin, Yao-Ting and Shen, Yu-Ching},
  title =	{{On the Impossibility of General Parallel Fast-Forwarding of Hamiltonian Simulation}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{33:1--33:45},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.33},
  URN =		{urn:nbn:de:0030-drops-183038},
  doi =		{10.4230/LIPIcs.CCC.2023.33},
  annote =	{Keywords: Hamiltonian simulation, Depth lower bound, Parallel query lower bound}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.17
Accelerating Polarization via Alphabet Extension

Authors: Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang

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

Abstract
Polarization is an unprecedented coding technique in that it not only achieves channel capacity, but also does so at a faster speed of convergence than any other technique. This speed is measured by the "scaling exponent" and its importance is three-fold. Firstly, estimating the scaling exponent is challenging and demands a deeper understanding of the dynamics of communication channels. Secondly, scaling exponents serve as a benchmark for different variants of polar codes that helps us select the proper variant for real-life applications. Thirdly, the need to optimize for the scaling exponent sheds light on how to reinforce the design of polar code. In this paper, we generalize the binary erasure channel (BEC), the simplest communication channel and the protagonist of many polar code studies, to the "tetrahedral erasure channel" (TEC). We then invoke Mori-Tanaka’s 2 × 2 matrix over 𝔽_4 to construct polar codes over TEC. Our main contribution is showing that the dynamic of TECs converges to an almost-one-parameter family of channels, which then leads to an upper bound of 3.328 on the scaling exponent. This is the first non-binary matrix whose scaling exponent is upper-bounded. It also polarizes BEC faster than all known binary matrices up to 23 × 23 in size. Our result indicates that expanding the alphabet is a more effective and practical alternative to enlarging the matrix in order to achieve faster polarization.
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Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang. Accelerating Polarization via Alphabet Extension. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{duursma_et_al:LIPIcs.APPROX/RANDOM.2022.17,
  author =	{Duursma, Iwan and Gabrys, Ryan and Guruswami, Venkatesan and Lin, Ting-Chun and Wang, Hsin-Po},
  title =	{{Accelerating Polarization via Alphabet Extension}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{17:1--17:15},
  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.2022.17},
  URN =		{urn:nbn:de:0030-drops-171393},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.17},
  annote =	{Keywords: polar code, scaling exponent}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.50
Tight Competitive Analyses of Online Car-Sharing Problems

Authors: Ya-Chun Liang, Kuan-Yun Lai, Ho-Lin Chen, and Kazuo Iwama

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
The car-sharing problem, proposed by Luo, Erlebach and Xu in 2018, mainly focuses on an online model in which there are two locations: 0 and 1, and k total cars. Each request which specifies its pick-up time and pick-up location (among 0 and 1, and the other is the drop-off location) is released in each stage a fixed amount of time before its specified start (i.e. pick-up) time. The time between the booking (i.e. released) time and the start time is enough to move empty cars between 0 and 1 for relocation if they are not used in that stage. The model, called kS2L-F, assumes that requests in each stage arrive sequentially regardless of the same booking time and the decision (accept or reject) must be made immediately. The goal is to accept as many requests as possible. In spite of only two locations, the analysis does not seem easy and the (tight) competitive ratio (CR) is only known to be 2.0 for k = 2 and 1.5 for a restricted value of k, i.e., a multiple of three. In this paper, we remove all the holes of unknown CR’s; namely we prove that the CR is 2k/(k + ⌊k/3⌋) for all k ≥ 2. Furthermore, if the algorithm can delay its decision until all requests have come in each stage, the CR is improved to roughly 4/3. We can take this advantage even further, precisely we can achieve a CR of (2+R)/3 if the number of requests in each stage is at most Rk, 1 ≤ R ≤ 2, where we do not have to know the value of R in advance. Finally we demonstrate that randomization also helps to get (slightly) better CR’s.
Cite as

Ya-Chun Liang, Kuan-Yun Lai, Ho-Lin Chen, and Kazuo Iwama. Tight Competitive Analyses of Online Car-Sharing Problems. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{liang_et_al:LIPIcs.ISAAC.2021.50,
  author =	{Liang, Ya-Chun and Lai, Kuan-Yun and Chen, Ho-Lin and Iwama, Kazuo},
  title =	{{Tight Competitive Analyses of Online Car-Sharing Problems}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.50},
  URN =		{urn:nbn:de:0030-drops-154835},
  doi =		{10.4230/LIPIcs.ISAAC.2021.50},
  annote =	{Keywords: Car-sharing, Competitive analysis, On-line scheduling, Randomized algorithm}
}
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