One way to choose a basis of a matroid at random is to choose an ordering of the ground set uniformly at random and then use the greedy algorithm to find a basis. We investigate the class of matroids having the property that this procedure yields a basis uniformly at random. We show how this class is related to some other naturally-defined families of matroids and consider how it behaves under ...

The randomized k-paging algorithm Equitable given by Achlioptas et al. is Hk-competitive and uses O(k 2 log k) memory. This competitive ratio is best possible. The randomized algorithm RMark given by Fiat et al. is (2Hk − 1)-competitive, but only uses O(k) memory. Borodin and El Yaniv [6] list as an open question whether there exists an Hk-competitive randomized algorithm which requires O(k) me...

In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NPcomplete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform proces...

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck/ log∗ k pairs of parts which are not -regular, where c, > 0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemerédi’s regularity lemma. In order to gain some control ...

Many multiagent settings require a collection of agents to partition themselves into coalitions. In such cases, the agents may have conflicting preferences over the possible coalition structures that may form. We investigate a noncooperative bargaining game to allow the agents to resolve such conflicts and partition themselves into non-overlapping coalitions. The game has a finite horizon and i...

Virulence functions of pathogenic bacteria are often encoded on large extrachromosomal plasmids. These plasmids are maintained at low copy number to reduce the metabolic burden on their host. Low-copy-number plasmids risk loss during cell division. This is countered by plasmid-encoded systems that ensure that each cell receives at least one plasmid copy. Plasmid replication and recombination ca...

In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence of the effectiveness of including these inequalities as cuts in a Branch & Cut algorithm.