We present an NC approximation algorithm for the weighted matching problem in graphs with an approximation ratio of (1 - ). This improves the previously best approximation ratio of...
Finding the largest independent set in a graph is a notoriously difficult NP-complete combinatorial optimization problem. Moreover, even for graphs with largest degree 3, no polyn...
We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the s...
We prove the existence of -Nash equilibrium strategies with support logarithmic in the number of pure strategies. We also show that the payoffs to all players in any (exact) Nash...
Richard J. Lipton, Evangelos Markakis, Aranyak Meh...
In unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters, such as the number of vertices, maximum degree, and aver...