We study the two-dimensional version of the bin packing problem with conflicts. We are given a set of (two-dimensional) squares V = {1, 2, . . . , n} with sides s1, s2 . . . , sn ...
Graph H is a root of graph G if there exists a positive integer k such that x and y are adjacent in G if and only if their distance in H is at most k. Motwani and Sudan [1994] prov...
Cooper, Dyer and Frieze studied the problem of sampling H-colourings (nearly) uniformly at random. Special cases of this problem include sampling colourings and independent sets a...
We consider the problem of finding a maximum independent set in a random graph. The random graph G, which contains n vertices, is modelled as follows. Every edge is included inde...
We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...