This work presents a Boolean satisfiability (SAT) encoding for a special problem from combinatorial optimization. In the last years much progress has been made in the optimization of practical SAT solvers (see the SAT competition [5]). This has made SAT encodings for combinatorial problems highly attractive. In this work we propose an encoding for the combinatorial problem Magic Labeling which ...

A version of the multiple unicast conjecture, proposed by M. Langberg and M. Médard [4], says that, there exists an undirected fractional multicommodity flow, or simply, multi-flow, with rate (1, 1, · · · , 1) for strongly reachable networks. In this paper, we propose a new type of matrix optimization problem to attack this conjecture: By giving upper and lower bounds on its solution, we prove ...

Given a simple graph G, we consider the node search problem with inert fugitive. We are interested in minimizing the maximum vertex occupation time, i.e. the maximum number of steps in which a vertex is occupied by a searcher during a search of G. We prove that a search program which does not allow a recontamination may not find an optimal solution to this problem. Moreover, the difference betw...

In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which r...

This paper presents a structural synthesis using the Mixed-Integer Non-Linear Programming (MINLP) approach. The MINLP is a combined discrete/continuous optimization technique, where discrete binary 0-1 variables are defined for optimization of discrete alternatives and continuous variables for optimization of parameters. The MINLP optimization to a structural synthesis is performed through thre...