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Abstract: this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 233, 267]. (Update)
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14: Computers and Intractability: A Guide to the Theory of NP-Completeness (context) - Garey, Johnson - 1979
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BibTeX entry: (Update)
I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999. http://citeseer.ist.psu.edu/article/bomze99maximum.html More
@incollection{ bomze99maximum,
author = "I. Bomze and M. Budinich and P. Pardalos and M. Pelillo",
title = "The maximum clique problem",
editor = "D.-Z. Du and P. M. Pardalos",
booktitle = "Handbook of Combinatorial Optimization",
volume = "4",
publisher = "Kluwer Academic Publishers, Boston, MA",
year = "1999",
url = "citeseer.ist.psu.edu/article/bomze99maximum.html" }
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951 Computational Complexity (context) - Papadimitriou - 1994
860 The Theory of Error Correcting Codes (context) - MacWilliams, Sloane - 1979
773 Reducibility among combinatorial problems (context) - Karp - 1972
704 Neural Networks: A Comprehensive Foundation (context) - Haykin - 1994
539 Computer Vision (context) - Ballard, Brown - 1982
518 Integer and Combinatorial Optimization (context) - Nemhauser, Wolsey - 1988
488 Algorithmic Graph Theory and Perfect Graphs (context) - Golumbic - 1980
474 Graph Theory (context) - Harary - 1969
417 Local Search in Combinatorial Optimization (context) - Aarts, Lenstra - 1997
411 Random graphs (context) - Bollob'as - 1985
403 Proof verification and hardness of approximation problems - Arora, Lund et al. - 1992
333 Geometric Algorithms and Combinatorial Optimization (context) - Grotschel, Lov'asz et al. - 1993
312 Tabu search---Part (context) - Glover - 1989
293 Approximation algorithms for combinatorial problems (context) - Johnson - 1974
272 Tabu search - Glover, Laguna - 1993
249 Molecular computation of solutions to combinatorial optimiza.. - Adleman - 1994
228 Simulated Annealing and Boltzmann Machines (context) - Aarts, Korst - 1989
218 Probabilistic construction of deterministic algorithms: Appr.. (context) - Raghavan - 1988
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206 Rinehart and Winston (context) - Lawler, Optimization et al. - 1976
178 Algorithmic aspects of vertex elimination on graphs (context) - Rose, Tarjan et al. - 1976
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173 An interiorpoint method for semidefinite programming - Helmberg, Rendl et al. - 1996
163 The complexity of enumeration and reliability problems (context) - Valiant - 1979
157 Advanced Combinatorics (context) - Comtet - 1974
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115 PCPs and nonapproximability ---Towards tight results (context) - Bellare, Goldreich et al. - 1997
112 New methods to color the vertices of a graph (context) - Brelaz - 1979
108 Improved nonapproximability results - Bellare, Sudan - 1994
104 approximation and complexity classes (context) - Papadimitriou, Yannakakis - 1991
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104 approximation and complexity classes (context) - Papadimitriou, Yannakakis - 1988
102 A fast and simple randomized parallel algorithm for the maxi.. (context) - Alon, Babai et al. - 1986
95 computation of decisions in optimization problems (context) - Hopfield, Tank - 1985
94 Interactive proofs and the hardness of approximating cliques - Feige, Goldwasser et al. - 1996
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85 the approximation of maximum satisfiability (context) - Yannakakis - 1992
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73 Recognizing and locating partially visible objects: The locu.. (context) - Bolles, Cain - 1982
73 Triangulated graphs and the elimination process (context) - Rose - 1970
72 Cones of matrices and set-functions and 0-1 optimization (context) - Lov'asz, Schrijver - 1991
72 On generating all maximal independent sets (context) - Johnson, Yannakakis et al. - 1988
71 Vertex packings: Structural properties and algorithms (context) - Nemhauser, Trotter - 1975
71 A fast parallel algorithm for the maximal independent set pr.. (context) - Karp, Wigderson - 1985
70 Introduction to the Theory of Complexity (context) - Bovet, Crescenzi - 1994
69 A greedy heuristic for the set-covering problem (context) - Chv'atal - 1979
64 Exploiting sparsity in primaldual interior-point methods for.. - Fujisawa, Kojima et al. - 1997
63 the complexity of approximating the independent set problem (context) - Berman, Schnitger - 1992
63 the complexity of approximating the independent set problem (context) - Berman, Schnitger - 1989
63 Algorithms for the maximum satisfiability problem (context) - Hansen, Jaumard - 1990
62 The maximum clique problem (context) - Pardalos, Xue - 1994
58 An exact algorithm for the maximum clique problem (context) - Carraghan, Pardalos - 1990
56 the Shannon capacity of a graph (context) - Lov'asz - 1979
56 the connection assignment problem of diagnosable systems (context) - Preparata, Metze et al. - 1967
53 Matching hierarchical structures using association graphs - Pelillo, Siddiqi et al. - 1998
50 Weakly triangulated graphs (context) - Hayward - 1985
49 Semidefinite programming in combinatorial optimization - Goemans - 1997
49 Algorithms for maximum independent sets (context) - Robson - 1986
47 Stereo correspondence through feature grouping and maximal c.. (context) - Horaud, Skordas - 1989
47 A new Table of constant weight codes (context) - Brouwer, Shearer et al. - 1990
45 Two prover protocols---Low error at affordable rates (context) - Feige, Kilian - 1994
44 Evolutionary Games and Population Dynamics (context) - Hofbauer, Sigmund - 1998
41 Spectra of Graphs (context) - Cvetkovi'c, Doob et al. - 1980
41 Arboricity and subgraph listing algorithms (context) - Chiba, Nishizeki - 1985
40 A greedy randomized adaptive search procedure for maximum in.. (context) - Feo, Resende et al. - 1994
38 Finding a maximum clique in an arbitrary graph (context) - Balas, Yu - 1986
38 and maximum independent set of a chordal graph (context) - Gavril, minimum et al. - 1972
35 Eigenvalues in combinatorial optimization (context) - Mohar, Poljak - 1993
35 Polynomial algorithms for perfect graphs (context) - Grotschel, Lov'asz et al. - 1989
34 A new parallel algorithm for the maximal independent set pro.. - Goldberg, Spencer - 1989
34 DPO: A three-dimensional part orientation system (context) - Bolles, Horaud - 1986
33 Derandomized graph products - Alon, Feige et al. - 1995
32 Large cliques elude the Metropolis process (context) - Jerrum - 1992
32 Reactive local search for the maximum clique problem - Battiti, Protasi - 1995
31 Testing of the long code and hardness clique (context) - Hastad - 1996
31 on and M.A. Trick (eds.), Cliques, Coloring, and Satisfiabil.. (context) - Johns - 1996
30 The sandwich theorem - Knuth - 1994
30 Modern graph theory (context) - Bollob'as - 1998
30 Object-oriented implementation of heuristic search methods f.. (context) - Fleurent, Ferland - 1996
29 an extremal problem in graph theory (context) - Tur'an - 1941
28 Finding a maximum independent set (context) - Tarjan, Trojanowski - 1977
28 Dual quadratic estimates in polynomial and Boolean programmi.. (context) - Shor - 1990
27 On certain polytopes associated with graphs (context) - Chv'atal - 1975
27 Branch and bound methods (context) - Balas, Toth - 1985
26 A continuous based heuristic for the maximum clique problem (context) - Gibbons, Hearn et al. - 1996
25 Continuous characterizations of the maximum clique problem - Gibbons, Hearn et al. - 1997
25 Quantifiers and approximation (context) - Panconesi, Ranjan - 1993
24 Efficient algorithms for interval graphs and circular-arc gr.. (context) - Gupta, Lee et al. - 1982
24 On maximum clique problems in very large graphs - Abello, Pardalos et al. - 1999
23 Evolutionary approach to the maximum clique problem: Empiric.. (context) - Bomze, Pelillo et al. - 1997
23 On maximal independent sets of vertices in claw-free graphs (context) - Minty - 1980
23 Efficient parallel algorithms for chordal graphs - Klein - 1988
22 Properties of vertex packings and independence system polyhe.. (context) - Nemhauser, Trotter - 1974
22 DNA solutions of the maximal clique problem (context) - Ouyang, Kaplan et al. - 1997
20 Algorithms and Complexity - Wilf - 1986
20 Neural Network Parallel Computing (context) - Takefuji - 1992
19 Finding maximum cliques in arbitrary and in special graphs (context) - Babel - 1991
19 Weighted and unweighted maximum clique algorithms with upper.. (context) - Balas, Xue - 1996
19 Polyhedral methods for the maximum clique problem (context) - Balas, Ceria et al. - 1996
19 Evolution towards the maximum clique (context) - Bomze - 1997
18 A branch and bound algorithm for the maximum clique problem (context) - Pardalos, Rodgers - 1992
18 The Lov'asz theta function and a semidefinite programming re.. - Kleinberg, Goemans - 1997
18 Computational aspects of a branch and bound algorithm for qu.. (context) - Pardalos, Rodgers - 1990
18 Finding a large hidden clique in a random graph - Alon, Krivelevich et al. - 1998
17 A branch and bound algorithm for the maximum clique problem (context) - Babel, Tinhofer - 1990
17 A versatile computer-controlled assembly system (context) - Ambler, Barrow et al. - 1973
17 matching relational structures and maximal cliques (context) - Barrow, Burstall et al. - 1976
16 Maxima for graphs and a new proof of a theorem of Tur (context) - Motzkin, Straus - 1965
16 Algorithms for a maximum clique and a maximum independent se.. (context) - Gavril - 1973
16 STABULUS: A technique for finding stable sets in large graph.. (context) - Friden, Hertz et al. - 1989
16 The largest clique size in a random graph (context) - Matula - 1976
16 Motif recognition and alignment for many sequences by compar.. (context) - Vingron, Argos - 1991
16 Constructing a maximal independent set in parallel - Goldberg, Spencer - 1989
16 Relaxation labeling networks for the maximum clique problem - Pelillo - 1995
16 A strong cutting plane/branchand bound algorithm for node pa.. (context) - Nemhauser, Sigismondi - 1992
15 the independence number of random graphs (context) - Frieze - 1990
15 Image sequence analysis using relational structures (context) - Radig - 1984
15 On bounded queries and approximation - Chang, Gasarch et al. - 1997
15 Algorithm 457: Finding all cliques of an undirected graph (context) - Bron, Kerbosch - 1973
15 An approximation algorithm for the maximum independent set p.. (context) - Chiba, Nishizeki et al. - 1982
14 Fast parallel algorithms for chordal graphs (context) - Naor, Naor et al. - 1987
14 Cliques in Random Graphs (context) - Bollob'as, Erdos - 1976
13 Edge-maximal triangulated subgraphs and heuristics for the m.. (context) - Xue - 1994
13 Approximating Maximum Clique with a Hopfield Network - Jagota - 1995
13 Continuous approaches to discrete optimization problems (context) - Pardalos - 1996
13 Constructing cliques using restricted backtracking - Goldberg, Rivenburgh - 1996
13 Feasible and infeasible maxima in a quadratic program for ma.. - Pelillo, Jagota - 1995
13 Optimal chaining of CMOS transistors in a functional cell (context) - Wimer, Pinter et al. - 1987
12 the computational complexity of finding stable state vectors.. (context) - Godbeer, Lipscomb et al. - 1988
12 Solving the maximum clique problem using a tabu search appro.. (context) - Gendreau, Salvail et al. - 1993
11 the query complexity of clique size and maximum satisfiabili.. - Chang - 1996
11 An evolutionary heuristic for the maximum independent set pr.. - Back, Khuri - 1994
11 the vertex packing problem (context) - Houck - 1974
11 Weak bipolarizable graphs (context) - Olariu - 1989
11 Clique is hard to approximate within n 1\Gamma (context) - Hastad - 1996
11 Topics on Perfect Graphs (context) - Berge, Chv'atal - 1984
11 A property of 4-chromatic graphs and some remarks on critica.. (context) - Dirac - 1952
11 The use of maximum curvature points for the recognition of p.. (context) - Han, Jang - 1990
10 Approximately solving maximum clique using neural networks a.. - Jagota, Sanchis et al. - 1996
10 On standard quadratic optimization problems (context) - Bomze - 1998
10 Test case generators and computational results for the maxim.. (context) - Hasselberg, Pardalos et al. - 1993
10 A global optimization approach for solving the maximum cliqu.. (context) - Pardalos, Phillips - 1990
10 Certain results in coding theory for noisy channels (context) - Shannon - 1957
10 Polynomial algorithm to recognize a Meyniel graph (context) - Burlet, Fonlupt - 1984
10 Relaxations of vertex packing (context) - Grotschel, Lov'asz et al. - 1986
10 Optimization by neural networks (context) - Ramanujam, Sadayappan - 1988
9 Keller's cube-tiling conjecture is false in high dimensions - Lagarias, Shor - 1992
8 Tabu search algorithms for the maximum clique problem (context) - Soriano, Gendreau - 1996
8 Guaranteed convergence in a class of Hopfield networks (context) - Shrivastava, Dasgupta et al. - 1992
8 Stability in circular-arc-graphs (context) - Golumbic, Hammer - 1988
8 Algorithmic aspects of the generalized clique-transversal pr.. (context) - Chang, Chen et al. - 1996
8 Annealed replication: A new heuristic for the maximum clique.. - Bomze, Budinich et al. - 1998
8 Parallel algorithms for finding a near-maximum independent s.. (context) - Takefuji, Chen et al. - 1990
8 Parallel branch and bound algorithms for quadratic zero-one .. (context) - Pardalos, Rodgers - 1990
8 A simple heuristic based genetic algorithm for the maximum c.. - Marchiori - 1998
8 Finding large cliques in arbitrary graphs by bipartite match.. (context) - Balas, Niehaus - 1996
8 Minimizing the number of states in incompletely specified se.. (context) - Paull, Unger - 1959
8 the greedy heuristic for continuous covering and packing pro.. (context) - Fisher, Wolsey - 1982
8 Labeled point pattern matching by Delaunay triangulation and.. (context) - Ogawa - 1986
7 An optimal algorithm for finding a maximum independent set o.. (context) - Masuda, Nakajima - 1988
7 Artificial neural networks (context) - Peterson, Soderberg - 1997
7 How good are genetic algorithms at finding large cliques: An.. - Carter, Park - 1993
7 Pseudo-boolean functions and stability of graphs (context) - Ebenegger, Hammer et al. - 1984
7 Spectral bounds for the clique and independence numbers of g.. (context) - Wilf - 1986
7 Neural network methods in combinatorial optimization (context) - Looi - 1992
6 On linear systems with integral valued solutions (context) - Heller - 1957
6 geometry and algorithms (context) - Felsner, Mueller et al. - 1997
6 An interior point approach to the maximum independent set pr.. - Karmarkar, Ramakrishnan et al. - 1989
6 the perfect graph conjecture (context) - Meyniel - 1976
6 and graph isomorphism (context) - Pelillo, equations et al. - 1999
6 Finding a maximum clique (context) - Tarjan - 1972
6 A sublinear-time randomized parallel algorithm for the maxim.. - Alizadeh - 1991
6 Algorithms on circular arc graphs (context) - Gavril - 1974
6 Algebraic tiling (context) - Stein - 1974
6 A parallel computation network for the maximum clique proble.. (context) - Lin, Lee - 1992
6 TABARIS: An exact algorithm based on tabu search for finding.. (context) - Friden, Hertz et al. - 1990
6 Applying the INN model to the max clique problem - Grossman
5 Clique finding---A genetic approach (context) - Murthy, Parthasarathy et al. - 1994
5 Computing independent sets in graphs with large girth (context) - Murphy - 1992
5 Diversification strategies in tabu search algorithms for the.. (context) - Soriano, Gendreau - 1996
5 Matching feature points in image sequences through a region-.. (context) - Pla, Marchant - 1997
5 A linear algorithm for maximum weight cliques in proper circ.. (context) - Bhattacharya, Hell et al. - 1996
5 Some experimental and theoretical results on test case gener.. (context) - Sanchis, Jagota - 1996
5 Neural network solutions to a graph theoretic problem (context) - Shrivastava, Dasgupta et al. - 1990
5 Israel Journal of Mathematics (context) - Moon, Moser et al. - 1965
5 A clique problem equivalent to graph isomorphism (context) - Kozen - 1978
5 Perfectly orderable graphs (context) - Chv'atal - 1985
5 Experiments with polynomial-time CLIQUE approximation algori.. (context) - Homer, Peinado - 1996
5 algorithm for the maximum clique problem in circular-arc gra.. (context) - Bhattacharya, Kaller et al. - 1997
5 Some polynomial algorithms for certain graphs and hypergraph.. (context) - Frank - 1976
5 Camouflaging independent sets in quasi-random graphs - Brockington, Culberson - 1996
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