The quantum guesswork quantifies the minimum number of queries needed to guess state a ensemble if one is allowed query only at time. Previous approaches computation were based on standard semi-definite programming techniques and therefore lead approximated results. In contrast, we show that computing qubit ensembles with uniform probability distribution corresponds solving quadratic assignment...

The quadratic assignment problem (QAP) was first proposed by Koopmans and Beckman [5] in the context of the plant location problem. Given n facilities, represented by the set F f1 fn , and n locations represented by the set L l1 ln , one must determine to which location each facility must be assigned. Let An n ai j be a matrix where ai j represents the flow between facilities fi and f j. Let Bn...

Several real-life applications can be stated in terms of the Quadratic Assignment Problem. Finding an optimal assignment is computationally very difficult, for many useful instances. We address this problem using a local search technique, based on Extremal Optimization and present experimental evidence that this approach is competitive. Moreover, cooperative parallel versions of our solver impr...

The Quadratic Assignment Problem (QAP) is an NP-complete problem. Different algorithms have been proposed using different methods. In this paper, the problem is formulated as a minimizing problem of a quadratic function with restrictions incorporated to the computational dynamics and variables Si {1,2,..., n}. To solve this problem a recurrent neural network multivalued (RNNM) is proposed. We ...

We obtain a number of results regarding the distribution of values of a quadratic function f on the set of n × n permutation matrices (identified with the symmetric group Sn) around its optimum (minimum or maximum). In particular, we estimate the fraction of permutations σ such that f(σ) lies within a given neighborhood of the optimal value of f . We identify some “extreme” functions f (there a...

In this paper, we present a simple algorithm to obtain mechanically SDP relaxations for any quadratic or linear program with bivalent variables, starting from an existing linear relaxation of the considered combinatorial problem. A significant advantage of our approach is that we obtain an improvement on the linear relaxation we start from. Moreover, we can take into account all the existing th...

In this paper, we consider partial Lagrangian relaxations of continuous quadratic formulations of the Quadratic Assignment Problem (QAP) where the assignment constraints are not relaxed. These relaxations are a theoretical limit for semidefinite relaxations of the QAP using any linearized quadratic equalities made from the assignment constraints. Using this framework, we survey and compare stan...