Document

PACE Solver Description

**Published in:** LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

A directed graph is formed by vertices and arcs from one vertex to another. The feedback vertex set problem (FVSP) consists in making a given directed graph acyclic by removing as few vertices as possible. In this write-up, we outline the core techniques used in the heuristic feedback vertex set algorithm, submitted to the heuristic track of the 2022 PACE challenge.

YuMing Du, QingYun Zhang, JunZhou Xu, ShunGen Zhang, Chao Liao, ZhiHuai Chen, ZhiBo Sun, ZhouXing Su, JunWen Ding, Chen Wu, PinYan Lu, and ZhiPeng Lv. PACE Solver Description: Hust-Solver - A Heuristic Algorithm of Directed Feedback Vertex Set Problem. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 29:1-29:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{du_et_al:LIPIcs.IPEC.2022.29, author = {Du, YuMing and Zhang, QingYun and Xu, JunZhou and Zhang, ShunGen and Liao, Chao and Chen, ZhiHuai and Sun, ZhiBo and Su, ZhouXing and Ding, JunWen and Wu, Chen and Lu, PinYan and Lv, ZhiPeng}, title = {{PACE Solver Description: Hust-Solver - A Heuristic Algorithm of Directed Feedback Vertex Set Problem}}, booktitle = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)}, pages = {29:1--29:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-260-0}, ISSN = {1868-8969}, year = {2022}, volume = {249}, editor = {Dell, Holger and Nederlof, Jesper}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.29}, URN = {urn:nbn:de:0030-drops-173855}, doi = {10.4230/LIPIcs.IPEC.2022.29}, annote = {Keywords: directed feedback vertex set, local search, simulated annealing, set covering} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

In the k-outconnected directed Steiner tree problem (k-DST), we are given an n-vertex directed graph G = (V,E) with edge costs, a connectivity requirement k, a root r ∈ V and a set of terminals T ⊆ V. The goal is to find a minimum-cost subgraph H ⊆ G that has k edge-disjoint paths from the root vertex r to every terminal t ∈ T. The problem is NP-hard, and inapproximability results are known in several parameters, e.g., hardness in terms of n: log^{2-ε}n-hardness for k = 1 [Halperin and Krauthgamer, STOC'03], 2^{log^{1-ε}n}-hardness for general case [Cheriyan, Laekhanukit, Naves and Vetta, SODA'12], hardness in terms of k [Cheriyan et al., SODA'12; Laekhanukit, SODA'14; Manurangsi, IPL'19] and hardness in terms of |T| [Laekhanukit, SODA'14].
In this paper, we show the approximation hardness of k-DST for various parameters.
- Ω(|T|/log |T|)-approximation hardness, which holds under the standard complexity assumption NP≠ ZPP. The inapproximability ratio is tightened to Ω(|T|) under the Strongish Planted Clique Hypothesis [Manurangsi, Rubinstein and Schramm, ITCS 2021]. The latter hardness result matches the approximation ratio of |T| obtained by a trivial approximation algorithm, thus closing the long-standing open problem.
- Ω(2^{k/2} / k)-approximation hardness for the general case of k-DST under the assumption NP≠ZPP. This is the first hardness result known for survivable network design problems with an inapproximability ratio exponential in k.
- Ω((k/L)^{L/4})-approximation hardness for k-DST on L-layered graphs for L ≤ O(log n). This almost matches the approximation ratio of O(k^{L-1}⋅ L ⋅ log |T|) achieved in O(n^L)-time due to Laekhanukit [ICALP'16].
We further extend our hardness results in terms of |T| to the undirected cases of k-DST, namely the single-source k-vertex-connected Steiner tree and the k-edge-connected group Steiner tree problems. Thus, we obtain Ω(|T|/log |T|) and Ω(|T|) approximation hardness for both problems under the assumption NP≠ ZPP and the Strongish Planted Clique Hypothesis, respectively. This again matches the upper bound obtained by trivial algorithms.

Chao Liao, Qingyun Chen, Bundit Laekhanukit, and Yuhao Zhang. Almost Tight Approximation Hardness for Single-Source Directed k-Edge-Connectivity. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 89:1-89:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{liao_et_al:LIPIcs.ICALP.2022.89, author = {Liao, Chao and Chen, Qingyun and Laekhanukit, Bundit and Zhang, Yuhao}, title = {{Almost Tight Approximation Hardness for Single-Source Directed k-Edge-Connectivity}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {89:1--89:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.89}, URN = {urn:nbn:de:0030-drops-164309}, doi = {10.4230/LIPIcs.ICALP.2022.89}, annote = {Keywords: Directed Steiner Tree, Hardness of Approximation, Fault-Tolerant and Survivable Network Design} }

Document

RANDOM

**Published in:** LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph.

Chao Liao, Jiabao Lin, Pinyan Lu, and Zhenyu Mao. Counting Independent Sets and Colorings on Random Regular Bipartite Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{liao_et_al:LIPIcs.APPROX-RANDOM.2019.34, author = {Liao, Chao and Lin, Jiabao and Lu, Pinyan and Mao, Zhenyu}, title = {{Counting Independent Sets and Colorings on Random Regular Bipartite Graphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)}, pages = {34:1--34:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-125-2}, ISSN = {1868-8969}, year = {2019}, volume = {145}, editor = {Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.34}, URN = {urn:nbn:de:0030-drops-112498}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.34}, annote = {Keywords: Approximate counting, Polymer model, Hardcore model, Coloring, Random bipartite graphs} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail