We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation associated to the dynamic program can be obtained from extended formulations of single-node flow polytopes. Given these results, we present a unary expansion-based...

We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happ...

Joint object matching, also known as multi-image namely, the problem of finding consistent partial maps among all pairs objects within a collection, is crucial task in many areas computer vision. This subsumes bipartite graph matching and partitioning special cases NP-hard, general. We develop scalable linear programming (LP) relaxations with theoretical performance guarantees for joint matchin...

In recent years we have seen the development of successful methods for solving optimization problems by integrating techniques from Constraint Programming (CP) and Operations research (OR). Such hybrid approaches draw the individual strengths of these different paradigms: OR heavily relies on mathematical programming formulations such as integer and linear programming, while CP uses constrained...

This paper discusses a logic programming (LP) paradigm and accompanying semantic foundations for specifying constraints and preferences. While the use of constraints in LP languages is well-known, we show that preferences are also natural and are useful in logical speciication of optimization and relaxation problems which arise in many applications involving constraints, e.g., engineering desig...

We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the SheraliAdams (SA), Lovász-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC) problem, a variation of the classic Vertex-Cover problem in which only t edges need to be covered. t-PVC admits a 2-approximation using various algorithmic techn...

We study the problem of computing the minimum vertex cover on k-uniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For general k, the problem was studied by Lovász [23], who gave a k 2 -approximation based on the standard LP relaxation. Subsequent work by Aharoni, Holzman and Krivelevich [1] show...

The one-dimensional cutting stock problem (1D-CSP) and the twodimensional two-stage guillotine constrained cutting problem (2D-2CP) are considered in this paper. The Gilmore-Gomory model of these problems has a very strong continuous relaxation which provides a good bound in an LP-based solution approach. In recent years, there have been several efforts to attack the one-dimensional problem by ...

We propose exact hybrid methods based on integer linear programming and constraint programming for an integrated employee timetabling and job-shop scheduling problem. Each method we investigate uses a constraint programming (CP) formulation associated with a linear programming (LP) relaxation. Under a CP framework, the LP-relaxation is integrated into a global constraint using in addition reduc...