Constant Approximating k-Clique Is W[1]-Hard

被引：7
|
作者：
Lin, Bingkai [1 ]
机构：
[1] Nanjing Univ, State Key Lab Novel Software Technol, Nanjing, Peoples R China
来源：
STOC '21: PROCEEDINGS OF THE 53RD ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING | 2021年
基金：
国家重点研发计划;
关键词：
FPT-Inapproximability; k-Clique; W[1]-hard; k-Vector-Sum; PARAMETERIZED COMPLEXITY; HARDNESS; PROOFS;
D O I：
10.1145/3406325.3451016
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
For every graph G, let omega(G) be the largest size of complete subgraph in G. This paper presents a simple algorithm which, on input a graph G, a positive integer k and a small constant epsilon > 0, outputs a graph G' and an integer k' in 2(Theta(k5)) . vertical bar G vertical bar(O(1))-time such that (1) k' <= 2(Theta)((k5)), (2) if omega(G) >= k, then omega(G') >= k', (3) if omega(G) < k, then omega(G') < (1-epsilon)k'. This implies that no f (k) . vertical bar G vertical bar(O(1))-time algorithm can distinguish between the cases omega(G) >= k and omega(G) < k/c for any constant c >= 1 and computable function f, unless FPT = W [1].
引用
收藏
页码：1749 / 1756
页数：8
相关论文
共 50 条
  • [41] Remarks on k-Clique, k-Independent Set and 2-Contamination in Complementary Prisms
    Camargo, Priscila P.
    Souza, Ueverton S.
    Nascimento, Julliano R.
    INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, 2021, 32 (01) : 37 - 52
  • [42] The Critical Point of k-Clique Percolation in the Erdős–Rényi Graph
    Gergely Palla
    Imre Derényi
    Tamás Vicsek
    Journal of Statistical Physics, 2007, 128 : 219 - 227
  • [43] Clustering of SSH Brute-Force Attack Logs Using k-Clique Percolation
    Studiawan, Hudan
    Pratomo, Baskoro Adi
    Anggoro, Radityo
    PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE ON INFORMATION & COMMUNICATION TECHNOLOGY AND SYSTEMS (ICTS), 2016, : 39 - 42
  • [44] Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts
    Esmaeel Moradi
    Balabhaskar Balasundaram
    Optimization Letters, 2018, 12 : 1947 - 1957
  • [45] Identifying and evaluating the internet opinion leader community based on k-clique clustering
    Weizhe Zhang
    Hui He
    Boran Cao
    Neural Computing and Applications, 2014, 25 : 595 - 602
  • [46] Heterogeneous quantum computing for satellite constellation optimization: solving the weighted k-clique problem
    Bass, Gideon
    Tomlin, Casey
    Kumar, Vaibhaw
    Rihaczek, Pete
    Dulny, Joseph, III
    QUANTUM SCIENCE AND TECHNOLOGY, 2018, 3 (02):
  • [47] Automatic Generation of Opaque Constants Based on the K-Clique Problem for Resilient Data Obfuscation
    Tiella, Roberto
    Ceccato, Mariano
    2017 IEEE 24TH INTERNATIONAL CONFERENCE ON SOFTWARE ANALYSIS, EVOLUTION, AND REENGINEERING (SANER), 2017, : 182 - 192
  • [48] Mining Periodic k-Clique from Real-World Sparse Temporal Networks
    Ren, Zebin
    Qin, Hongchao
    Li, Rong-Hua
    Dai, Yongheng
    Wang, Guoren
    Li, Yanhui
    WEB AND BIG DATA, PT I, APWEB-WAIM 2022, 2023, 13421 : 461 - 476
  • [49] An Overlapping Community Discovery Algorithm Based on Label Propagation Constructing a K-Clique Network
    Xu, Xinqi
    Zheng, Xiaoyan
    2022 IEEE THE 5TH INTERNATIONAL CONFERENCE ON BIG DATA AND ARTIFICIAL INTELLIGENCE (BDAI 2022), 2022, : 232 - 236
  • [50] KClist++: A Simple Algorithm for Finding k-Clique Densest Subgraphs in Large Graphs
    Sun, Bintao
    Danisch, Maximilien
    Chan, T-H Hubert
    Sozio, Mauro
    PROCEEDINGS OF THE VLDB ENDOWMENT, 2020, 13 (10): : 1628 - 1640
12345