Sinkhorn Algorithm for Lifted Assignment Problems

An Algorithm for Fractional Assignment Problems

In this paper, we propose a polynomial time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I; J;E) be a bipartite graph where I and J are vertex sets and E I J is an edge set. We call an edge subset X( E) an assignment if every vertex is incident to exactly one edge from X: Given an integer weight c ij and a positive integer w...

The Sinkhorn-Knopp Algorithm: Convergence and Applications

As long as a square nonnegative matrix A contains sufficient nonzero elements, then the Sinkhorn-Knopp algorithm can be used to balance the matrix, that is, to find a diagonal scaling of A that is doubly stochastic. It is known that the convergence is linear and an upper bound has been given for the rate of convergence for positive matrices. In this paper we give an explicit expression for the ...

A New Approach for Solving Grey Assignment Problems

Linear assignment problem is one of the most important practical models in the literature of linear programming problems‎. ‎Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach‎. ‎In this way‎, ‎some researchers have used a whitening technique to solve the grey assignment p...

Lifted Junction Tree Algorithm

Hybrid Meta-heuristic Algorithm for Task Assignment Problem

Task assignment problem (TAP) involves assigning a number of tasks to a number of processors in distributed computing systems and its objective is to minimize the sum of the total execution and communication costs, subject to all of the resource constraints. TAP is a combinatorial optimization problem and NP-complete. This paper proposes a hybrid meta-heuristic algorithm for solving TAP in a ...