In this paper, we are interested inminimizing the sum of block sizes in a pairwise balanced design, where there are some constraints on the size of one block or the size of the largest block. For every positive integers n,m, wherem ≤ n, letS (n,m) be the smallest integer s for which there exists a PBD on n points whose largest block has sizem and the sum of its block sizes is equal to s. Also, ...

In this paper we study the set cover games when the elements are selfish agents. In this case, each element has a privately known valuation of receiving the service from the sets, i.e., being covered by some set. Each set is assumed to have a fixed cost. We develop several approximately efficient strategyproof mechanisms, each of which decides, after soliciting the declared bids by all elements...

For an unmixed bipartite graph G we consider the lattice of vertex covers LG and compute depth, projective dimension and extremal Bettinumbers of R/I(G) in terms of this lattice.

We analyse a newspaper market where two editors compete for advertising as well as for readership. They first choose the political position of their newspaper, then set cover prices and advertising tariffs. We build on the work of Gabszewicz, Laussel and Sonnac (2001, 2002), whose model we take as the stage game of an infinitely repeated game, and investigate the incentives to collude and the p...

Protein crystallization screens frequently yield salt crystals as well as protein crystals. A simple method for determining whether a crystal is composed of salt or macromolecules is suggested. A drop containing one or more crystals is transferred to a glass cover slip and the cover slip is then passed through the flame of a Bunsen burner. Macromolecule crystals are destroyed by this treatment,...

The paper is about the edge covers of the graph. The change in the edge covering number of the graph is observed under the operations vertex removal, edge removal and edge addition. The necessary and sufficient condition is proved under which the edge covering number decreases when a vertex is removed from the graph also when an edge is added to the graph. The necessary and sufficient condition...

In the k-supplier problem, we are given a set of clients C and set of facilities F located in a metric (C∪F, d), along with a bound k. The goal is to open a subset of k facilities so as to minimize the maximum distance of a client to an open facility, i.e., minS⊆F :|S|=k maxv∈C d(v, S), where d(v, S) = minu∈S d(v, u) is the minimum distance of client v to any facility in S. We present a 1 + √ 3...

We investigate the question of which graphs have planar emulators (a locally-surjective homomorphism from some finite planar graph)—a problem raised already in Fellows’ thesis (1985) and conceptually related to the better known planar cover conjecture by Negami (1986). For over two decades, the planar emulator problem lived poorly in a shadow of Negami’s conjecture—which is still open—as the tw...

Surface exposure ages of glacial deposits in the Ford Ranges of western Marie Byrd Land indicate continuous thinning of the West Antarctic Ice Sheet by more than 700 meters near the coast throughout the past 10,000 years. Deglaciation lagged the disappearance of ice sheets in the Northern Hemisphere by thousands of years and may still be under way. These results provide further evidence that pa...