Min Sum Set Cover and its Generalizations Name: Sungjin Im Affil./Addr. Electrical Engineering and Computer Science, University of California, Merced, CA, USA

We describe an elegant O * (2 k) algorithm for the disjoint compression problem for Odd Cycle Transver-sal based on a reduction to Above Guarantee Vertex Cover. We believe that this algorithm refines the understanding of the Odd Cycle Transversal algorithm by Reed, Smith and Vetta [RSV04].

In this paper we study the set cover games when the elements are selfish agents, each of which 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 that decide, after soliciting the declared bids by all elements, which elements will be...

This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition or the cover pebbling definition is shown to be NP -complete. The problem of determining the cover pebbling number for an arbitrary demand configuration is ...

The VERTEX COVER problem asks, for input consisting of a graph G on n vertices, and a positive integer k, whether there is a set of k vertices such that every edge of G is incident with at least one of these vertices. We give an algorithm for this problem that runs in time O(kn + (1.324718)'k'). In particular, this gives an 0((1.324718) " n2) algorithm to find the minimum vertex cover in the gr...

Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the complement has a transitive orientation). The operation of “vertex splitting”, introduced in [3], f...

Let α(G) and β(G) be the independent number and vertex covering number of G, respectively. The Kronecker Product G1 ⊗ G2 of graph of G1 and G2 has vertex set V (G1 ⊗ G2) = V (G1) × V (G2) and edge set E(G1 ⊗ G2) = {(u1v1)(u2v2)|u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. In this paper, let G is a simple graph with order p, we prove that, α(Km,n⊗G)= max {(m+n)α(G),p max{m,n}} and β(Km,n⊗G) =min {(m + n)β(G)...

It is shown that the Hilbert series of the face ring of a clique complex (equivalently, flag complex) of a graph G is, up to a factor, just a specialization of S G (x, y), the subgraph polynomial of the complement of G. We also find a simple relationship between the size of a minimum vertex cover of a graph G and its subgraph polynomial. This yields a formula for the h-vector of the flag comple...

For the class of monotone boolean functions f : {0,1}n → {0,1} where all 1-certificates have size 2, we prove the tight bound n (λ+ 2)2/4, where λ is the size of the largest 0-certificate of f . This result can be translated to graph language as follows: for every graph G= (V ,E) the inequality |V | (λ+ 2)2/4 holds, where λ is the size of the largest minimal vertex cover of G. In addition, ther...

Using known results regarding PCP, we present simple proofs of the inapproximability of vertex cover for hypergraphs. Specifically, we