In this paper, we consider the problem of cluster task assignment to maximize total utilities of nodes for target coverage in heterogeneous Wireless Sensor Networks. We define this problem as assigning the tasks of Cluster Head (CH) and Cluster Members (CM) to nodes for each target and requiring communication connectivity between every CHwith its members. The utility of each node for each targe...

This paper introduces iterative relaxation abstraction (IRA), a new method for reachability analysis of LHA that aims to improve scalability by combining the capabilities of current tools for analysis of low-dimensional LHA with the power of linear programming (LP) for large numbers of constraints and variables. IRA is inspired by the success of counterexample guided abstraction refinement (CEG...

When scheduling its audit{sta , the management of an auditing rm encompasses a number of decisions. These may be grouped into several categories which di er markedly in terms of organizational echelon involved, length of the planning horizon and the planning periods, degree of aggregation of the audit tasks, degree of detail of the required information, and decision objective. In this paper we ...

The LP relaxation for the Priority Steiner Tree is similar to the relaxation used before for the Steiner Tree. Again, say a set S ⊆ V crosses the set R if S ∩ R 6= ∅ and R \S 6= ∅ there is at least one terminal in S and one not in S. For j ≤ k, let Sj be the collection of all sets which cross Rj . Finally, for a set S ⊆ V , let ∂S be the set of edges with one endpoint in S and one in V \S. Defi...

Dantzig-Wolfe reformulation of an integer program convexifies a subset of the constraints, which yields an extended formulation with a potentially stronger linear programming (LP) relaxation than the original formulation. This paper is part of an endeavor to understand the strength of such a reformulation in general. We investigate the strength of Dantzig-Wolfe reformulations of the classical e...

We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to max-product but unlike max-product it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable para...

In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. For instance, for Vertex Cover one can obtain a 2-approximation via this approach. On the other hand, Khot and Regev [KR08] proved that, assuming the Unique Games Conjecture (UGC), it is NP-hard t...

Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the cur...

This report constitutes the Doctoral Dissertation for Michael Perregaard and is a collection of results on the efficient generation of disjunctive cuts for mixed integer programs. Disjunctive cuts is a very broad class of cuts for mixed integer programming. In general, any cut that can be derived from a disjunctive argument can be considered a disjunctive cut. Here we consider specifically cuts...

The principal idea of this paper is to exploit Semidefinite Programming (SDP) relaxation within the framework provided by Mixed Integer Nonlinear Programming (MINLP) solvers when tackling Binary Quadratic Problems (BQP). SDP relaxation is well-known to provide strong bounds for BQP in practice. However, the method is not typically implemented in many state-of-the-art MINLP solvers based on Line...