On Semidefinite Programming Relaxations for the Satisfiability Problem

This paper is concerned with the analysis and comparison of semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. Our presentation is focussed on the special case of 3-SAT, but the ideas presented can in principle be extended to any instance of SAT specified by a set of boolean variables and a propositional formula in … Read more

A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing

Intra-domain traffic engineering aims to make more efficient use of network resources within an autonomous system. Interior Gateway Protocols such as OSPF (Open Shortest Path First) and IS-IS (Intermediate System-Intermediate System) are commonly used to select the paths along which traffic is routed within an autonomous system. These routing protocols direct traffic based on link … Read more

Streaming Cache Placement Problems: Complexity and Algorithms

Virtual private networks (VPN) are often used to distribute live content, such as video or audio streams, from a single source to a large number of destinations. Streaming caches or splitters are deployed in these multicast networks to allow content distribution without overloading the network. In this paper, we consider two combinatorial optimization problems that … Read more

A Branch and Cut Algorithm for Hub Location Problems with Single Assignment

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. … Read more

The integer hull of a convex rational polytope

Given $A\in Z^{m\times n}$ and $b\in Z^m$, we consider the integer program $\max \{c’x\vert Ax=b;x\in N^n\}$ and provide an equivalent and explicit linear program $\max \{\widehat{c}’q\vert M q=r;q\geq 0\}$, where $M,r,\widehat{c}$ are easily obtained from $A,b,c$ with no calculation. We also provide an explicit algebraic characterization of the integer hull of the convex polytope $P=\{x\in\R^n\vert … Read more

Duality and a Farkas lemma for integer programs

We consider the integer program $\max \{c’ x\,|\,Ax=b,x\in N^n\}$. A formal parallel between linear programming and continuous integration on one side, and discrete summation on the other side, shows that a natural duality for integer programs can be derived from the $Z$-transform and Brion and Vergne’s counting formula. Along the same lines, we also provide … Read more

A methodology for the analysis of parallel GRASP strategies

In this paper, we describe a methodology for the analysis of greedy randomized adaptive search procedures (GRASP). GRASP is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and a local search. Hybrid approaches of GRASP with path-relinking developed for the 3-index assignment problem (AP3) and … Read more

GRASP and path-relinking: Recent advances and applications

This paper addresses recent advances and application of hybridizations of greedy randomized adaptive search procedures (GRASP) and path-relinking. We present a template for implementing path-relinking as an intensification procedure for GRASP. Enhancements to the procedure, recently described in the literature, are reviewed. The effectiveness of the procedure is illustrated experimentally. CitationAT&T Labs Research Technical Report, … Read more