5 Search Results for "Tsai, Shi-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)

Copy BibTex To Clipboard

@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)

Copy BibTex To Clipboard

@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.ISAAC.2023.50
On Min-Max Graph Balancing with Strict Negative Correlation Constraints

Authors: Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We consider the min-max graph balancing problem with strict negative correlation (SNC) constraints. The graph balancing problem arises as an equivalent formulation of the classic unrelated machine scheduling problem, where we are given a hypergraph G = (V,E) with vertex-dependent edge weight function p: E×V ↦ ℤ^{≥0} that represents the processing time of the edges (jobs). The SNC constraints, which are given as edge subsets C_1,C_2,…,C_k, require that the edges in the same subset cannot be assigned to the same vertex at the same time. Under these constraints, the goal is to compute an edge orientation (assignment) that minimizes the maximum workload of the vertices. In this paper, we conduct a general study on the approximability of this problem. First, we show that, in the presence of SNC constraints, the case with max_{e ∈ E} |e| = max_i |C_i| = 2 is the only case for which approximation solutions can be obtained. Further generalization on either direction, e.g., max_{e ∈ E} |e| or max_i |C_i|, will directly make computing a feasible solution an NP-complete problem to solve. Then, we present a 2-approximation algorithm for the case with max_{e ∈ E} |e| = max_i |C_i| = 2, based on a set of structural simplifications and a tailored assignment LP for this problem. We note that our approach is general and can be applied to similar settings, e.g., scheduling with SNC constraints to minimize the weighted completion time, to obtain similar approximation guarantees. Further cases are discussed to describe the landscape of the approximability of this prbolem. For the case with |V| ≤ 2, which is already known to be NP-hard, we present a fully-polynomial time approximation scheme (FPTAS). On the other hand, we show that the problem is at least as hard as vertex cover to approximate when |V| ≥ 3.
Cite as

Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao. On Min-Max Graph Balancing with Strict Negative Correlation Constraints. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kuo_et_al:LIPIcs.ISAAC.2023.50,
  author =	{Kuo, Ting-Yu and Chen, Yu-Han and Frosini, Andrea and Hsieh, Sun-Yuan and Tsai, Shi-Chun and Kao, Mong-Jen},
  title =	{{On Min-Max Graph Balancing with Strict Negative Correlation Constraints}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.50},
  URN =		{urn:nbn:de:0030-drops-193524},
  doi =		{10.4230/LIPIcs.ISAAC.2023.50},
  annote =	{Keywords: Unrelated Scheduling, Graph Balancing, Strict Correlation Constraints}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.84
Dependent k-Set Packing on Polynomoids

Authors: Meng-Tsung Tsai, Shi-Chun Tsai, and Tsung-Ta Wu

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Specialized hereditary systems, e.g., matroids, are known to have many applications in algorithm design. We define a new notion called d-polynomoid as a hereditary system (E, ℱ ⊆ 2^E) so that every two maximal sets in ℱ have less than d elements in common. We study the problem that, given a d-polynomoid (E, ℱ), asks if the ground set E contains 𝓁 disjoint k-subsets that are not in ℱ, and obtain a complexity trichotomy result for all pairs of k ≥ 1 and d ≥ 0. Our algorithmic result yields a sufficient and necessary condition that decides whether each hypergraph in some classes of r-uniform hypergraphs has a perfect matching, which has a number of algorithmic applications.
Cite as

Meng-Tsung Tsai, Shi-Chun Tsai, and Tsung-Ta Wu. Dependent k-Set Packing on Polynomoids. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 84:1-84:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{tsai_et_al:LIPIcs.MFCS.2023.84,
  author =	{Tsai, Meng-Tsung and Tsai, Shi-Chun and Wu, Tsung-Ta},
  title =	{{Dependent k-Set Packing on Polynomoids}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{84:1--84:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.84},
  URN =		{urn:nbn:de:0030-drops-186180},
  doi =		{10.4230/LIPIcs.MFCS.2023.84},
  annote =	{Keywords: Hereditary Systems, Hypergraph Matchings, Compleixty Trichotomy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.29
A Dichotomy Result for Cyclic-Order Traversing Games

Authors: Yen-Ting Chen, Meng-Tsung Tsai, and Shi-Chun Tsai

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Traversing game is a two-person game played on a connected undirected simple graph with a source node and a destination node. A pebble is placed on the source node initially and then moves autonomously according to some rules. Alice is the player who wants to set up rules for each node to determine where to forward the pebble while the pebble reaches the node, so that the pebble can reach the destination node. Bob is the second player who tries to deter Alice's effort by removing edges. Given access to Alice's rules, Bob can remove as many edges as he likes, while retaining the source and destination nodes connected. Under the guide of Alice's rules, if the pebble arrives at the destination node, then we say Alice wins the traversing game; otherwise the pebble enters an endless loop without passing through the destination node, then Bob wins. We assume that Alice and Bob both play optimally. We study the problem: When will Alice have a winning strategy? This actually models a routing recovery problem in Software Defined Networking in which some links may be broken. In this paper, we prove a dichotomy result for certain traversing games, called cyclic-order traversing games. We also give a linear-time algorithm to find the corresponding winning strategy, if one exists.
Cite as

Yen-Ting Chen, Meng-Tsung Tsai, and Shi-Chun Tsai. A Dichotomy Result for Cyclic-Order Traversing Games. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ISAAC.2018.29,
  author =	{Chen, Yen-Ting and Tsai, Meng-Tsung and Tsai, Shi-Chun},
  title =	{{A Dichotomy Result for Cyclic-Order Traversing Games}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.29},
  URN =		{urn:nbn:de:0030-drops-99775},
  doi =		{10.4230/LIPIcs.ISAAC.2018.29},
  annote =	{Keywords: st-planar graphs, biconnectivity, fault-tolerant routing algorithms, software defined network}
}
  • Refine by Author
  • 3 Tsai, Shi-Chun
  • 2 Tsai, Meng-Tsung
  • 1 Assadi, Sepehr
  • 1 Chen, Yen-Ting
  • 1 Chen, Yu-Han
  • Show More...

  • Refine by Classification
  • 1 Mathematics of computing → Graph theory
  • 1 Mathematics of computing → Matroids and greedoids
  • 1 Networks → Network reliability
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 1 Communication complexity
  • 1 Compleixty Trichotomy
  • 1 Computational Chemistry
  • 1 Graph Balancing
  • 1 Graph streaming
  • Show More...

  • Refine by Type
  • 5 document

  • Refine by Publication Year
  • 2 2023
  • 2 2024
  • 1 2018

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact