A set of points and a positive integer m are given and our goal is to cover the maximum number of these point with m disks. We devise the first output sensitive algorithm for this problem. We introduce a parameter ρ as the maximum number of points that one disk can cover. In this paper first we solve the problem for m = 2 in O(nρ + ρ log ρ)) time. The previous algorithm for this problem runs in...

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of e...

We investigate the problem of packing and covering odd (u, v)-trails in a graph. A (u, v)-trail is a (u, v)-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let ν(u, v) denote the maximum number of edge-disjoint odd (u, v)-trails, and τ(u, v) denote the minimum size of an edge-set that intersects every odd (u, ...

We de ne a natural product on integer programming problems with nonnegative coe cients. Hypergraph covering problems are a special case of such integer programs, and the product we de ne is a generalization of the usual hypergraph product. The main theorem of this paper gives a su cient condition under which the solution to the nth power of an integer program is asymptotically as good as the so...

We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an instance of the test covering problem with geometric constraints on the tests. We give tight lower and upper bounds on the number of disks needed to identify...

It is shown that any weakly-skew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natural read-once property. A 2 size lower bound is proven for ordered syntactically multilinear ABPs computing an...

Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusionexclusion ...

Using covering problems (CoP) combined with binary search is a well-known and successful solution approach for solving continuous center problems. In this paper, we show that this is also true for center hub location problems in networks. We introduce and compare various formulations for hub covering problems (HCoP) and analyse the feasibility polyhedron of the most promising one. Computational...

Given a set of polyhedral cones C1, · · · , Ck ⊂ R, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R or a given linear subspace R. As a consequence, we show that it is coNP-complete to decide if ...

The Conditional Covering Problem (CCP) aims to locate facilities on a graph, where the vertex set represents both the demand points and the potential facility locations. The problem has a constraint that each vertex can cover only those vertices that lie within its covering radius and no vertex can cover itself. The objective of the problem is to find a set that minimizes the sum of the facilit...