Analysis of an iterated local search algorithm for vertex cover in sparse random graphs

Recently, various randomized search heuristics have been studied for the solution of the minimum vertex cover problem, in particular for sparse random instances according to the G(n,c/n) model, where c>0 is a constant. Methods from statistical physics suggest that the problem is easy if c

[1]  B. Pittel,et al.  Maximum matchings in sparse random graphs: Karp-Sipser revisited , 1998 .

[2]  Frank Neumann,et al.  Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem , 2004, GECCO.

[3]  Frank Neumann,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Runtime Analysis of a Simple Ant Colony Optimization Algorithm Runtime Analysis of a Simple Ant Colony Optimization Algorithm , 2022 .

[4]  Ingo Wegener,et al.  Simulated Annealing Beats Metropolis in Combinatorial Optimization , 2005, ICALP.

[5]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[6]  Isaac K. Evans,et al.  Evolutionary Algorithms for Vertex Cover , 1998, Evolutionary Programming.

[7]  Martin Pelikan,et al.  Hybrid evolutionary algorithms on minimum vertex cover for random graphs , 2007, GECCO '07.

[8]  Frank Neumann,et al.  Analyses of Simple Hybrid Algorithms for the Vertex Cover Problem , 2009, Evolutionary Computation.

[9]  M. Bauer,et al.  Core percolation in random graphs: a critical phenomena analysis , 2001, cond-mat/0102011.

[10]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[11]  Alexander K. Hartmann,et al.  Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs , 2000, Theor. Comput. Sci..

[12]  Carsten Witt,et al.  Greedy Local Search and Vertex Cover in Sparse Random Graphs , 2009, TAMC.

[13]  Ingo Wegener,et al.  Randomized local search, evolutionary algorithms, and the minimum spanning tree problem , 2004, Theor. Comput. Sci..

[14]  Dirk Sudholt,et al.  Hybridizing Evolutionary Algorithms with Variable-Depth Search to Overcome Local Optima , 2011, Algorithmica.

[15]  Alan M. Frieze,et al.  Maximum matchings in sparse random graphs: Karp-Sipser revisited , 1998, Random Struct. Algorithms.

[16]  Richard M. Karp,et al.  Maximum Matchings in Sparse Random Graphs , 1981, FOCS 1981.

[17]  Ingo Wegener,et al.  Evolutionary Algorithms , Randomized Local Search , and the Maximum Matching Problem ∗ , 2003 .

[18]  D. Gamarnik,et al.  Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method , 2006 .

[19]  Béla Bollobás,et al.  Random Graphs , 1985 .

[20]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[21]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[22]  Dirk Sudholt,et al.  Running Time Analysis of ACO Systems for Shortest Path Problems , 2009, SLS.

[23]  Carsten Witt,et al.  UNIVERSITY OF DORTMUND REIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531 Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Worst-Case and Average-Case Approximations by Simple Randomized Search Heuristics , 2004 .

[24]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[25]  Robert E. Tarjan,et al.  Finding a Maximum Independent Set , 1976, SIAM J. Comput..

[26]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[27]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[28]  Frank Neumann,et al.  Approximating Covering Problems by Randomized Search Heuristics Using Multi-Objective Models , 2010, Evolutionary Computation.

[29]  M. Sipser,et al.  Maximum matching in sparse random graphs , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[30]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 1 , 1967 .