Contributed by Arun Jagota and Laura Sanchis. This package contains approximation algorithms for the maximum clique problem, based on neural network heuristics. For information about the algorithms see the following references: Arun Jagota, Laura Sanchis, and Ravikanth Ganesan, "Approximately Solving Maximum Clique using Neural Network and Related Heuristics", in "Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, 1993", edited by David S. Johnson and Michael A. Trick, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, to appear 1996. Laura A. Sanchis and Arun Jagota, "Some Experimental and Theoretical Results on Test Case Generators for the Maximum Clique Problem", INFORMS Journal on Computing, Volume 8, Number 2, pp. 103-117, 1996. There are four algorithms: ssd0 (stochastic steep descent with initial state = empty set) ssdv (stochastic steep descent with initial state = V) gsd0 (greedy steepest descent with initial state = empty set) gsdv (greedy steepest descent with initial state = V) To compile, use the Makefile, e.g. "make ssd0" To run: ssd0 filename is the name of the file containing the description of the input graph. goal is the size of the maximum clique; the algorithm will stop if this size clique is found. iterations is the number of iterations to run. At the end, the algorithm prints out the average clique size found over all iterations, the number of iterations run, the maximum clique size found over all iterations, and the iteration number at which the max was found. The input file is expected to have the following format: Line 1 holds five numbers: the number of vertices the number of edges the maximum clique size (if known, otherwise 0) 0 0 Each successive line lists the degree and adjacency list for a single vertex. Example: 10 20 3 0 0 6 1 2 5 7 8 9 4 0 3 5 6 5 0 4 5 6 9 3 1 6 7 3 2 7 8 3 0 1 2 4 1 2 3 7 6 0 3 4 6 8 9 3 0 4 7 3 0 2 7 This graph has 10 vertices and 20 edges. Vertices are numbered from 0 to 9. Vertex 0 is adjacent to vertices 1, 2, 5, 7, 8, and 9.