We study a semidefinite programming relaxation of the traveling salesman problem intro-duced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unboundedintegrality gap. In particular, we give a family of instances such that the gap increases linearlywith n. To obtain this result, we search for feasible solutions within a highly structured class of...

A major task of telecommunication network planners is deciding where spare capacity is needed, and how much, so that interrupted traffic may be rerouted in the event of a failure. Planning the spare capacity so as to minimize cost is an NP-hard problem, and for large networks, even the linear relaxation is too large to be solved with existing methods. The main contribution of this paper is a fa...

We consider the problem of scheduling n jobs with release dates on m identical parallel machines to minimize the average completion time of the jobs. We prove that the ratio of the average completion time of the optimal nonpreemptive schedule to that of the optimal preemptive schedule is at most 3 , improving a bound of (3− 1 m ) due to Phillips, Stein and Wein. We then use our technique to giv...

Given an undirected graph G = (V; E) and three speciied terminal nodes t1; t2; t3, a 3-cut is a subset A of E such that no two terminals are in the same component of GnA. If a non-negative edge weight ce is speciied for each e 2 E, the optimal 3-cut problem is to nd a 3-cut of minimum total weight. This problem is NP-hard, and in fact, is max-SNP-hard. An approximation algorithm having performa...

We formulate the problem of nonprojective dependency parsing as a polynomial-sized integer linear program. Our formulation is able to handle non-local output features in an efficient manner; not only is it compatible with prior knowledge encoded as hard constraints, it can also learn soft constraints from data. In particular, our model is able to learn correlations among neighboring arcs (sibli...

Loopy belief propagation has been employed in a wide variety of applications with great empirical success, but it comes with few theoretical guarantees. In this paper we investigate the use of the max-product form of belief propagation for weighted matching problems on general graphs. We show that max-product converges to the correct answer if the linear programming (LP) relaxation of the weigh...

In this paper, we provide an easily satisfied relaxation condition for the primaldual interior path-following algorithm to solve linear programming problems. It is shown that the relaxed algorithm preserves the property of polynomial-time convergence. The computational results obtained by implementing two versions of the relaxed algorithm with slight modifications clearly demonstrate the potent...

In the seventies, Balas introduced intersection cuts for a Mixed Integer Linear Program (MILP), and showed that these cuts can be obtained by a closed form formula from a basis of the standard linear programming relaxation. In the early nineties, Cook, Kannan and Schrijver introduced the split closure of an MILP, and showed that the split closure is a polyhedron. In this paper, we show that the...

We introduce computable a-priori and a-posteriori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the LP relaxation of a mixed integer linear optimization problem. Treating the mesh size of integer vectors as a parameter allows us to study the effect of different ‘granularities’ in the discrete variables on the error bounds. Our analysis m...