Informed search algorithms such as A* use heuristics to focus exploration on states with low total path cost. To the extent that heuristics underestimate forward costs, a wider cost radius of suboptimal states will be explored. For many weighted graphs, however, a small distance in terms of cost may encompass a large fraction of the unweighted graph. We present a new informed search algorithm, ...

This paper focuses on the following problems: Problem 1 Given an axis parallel rectangle, how do you cut it in k equal area pieces such that the total length of the cuts is minimum? What are the properties of an optimal cut? Problem 2 Given an axis parallel prism, how do you cut it in k equal volume pieces such that the total surface area of the cuts is minimum? What are the properties of an op...

We propose a new class of Foundation-Penalty (FP) cuts for GUB-constrained (and ordinary) mixed-integer programs, which are easy to generate by exploiting standard penalty calculations that are routinely employed in branch-and-bound contexts. The FP cuts are derived with reference to a selected integer variable or GUB set, and a foundation function that is typically a reduced cost function corr...

This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing semidefinite and quadratic programming relaxations and dominate existing cuts proposed in the literature. Combined with model intersection and bound tightening, the new l...

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual ellipsoids. The new primal and dual dir...

Combinatorial min-cut algorithms on graphs emerged as an increasingly useful tool for problems in vision. Typically, the use of graphcuts is motivated by one of the following two reasons. Firstly, graph-cuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a hypersurface in N-D space embedding the corresponding graph. Thus, many applications in vision and...