Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

One of the obstacles in a branch-and-cut IP-solving scheme is closing the gap between a known feasible solution and the solution(s) to LP relaxations of the problem. There are, however, a number of real-world problems, where, once an optimal solution is found, its optimality can easily be proved using neither branch-and-bound nor branch-and-cut methods. All one needs to do is find an integral s...

An uncovered bargaining solution is a bargaining solution for which there exists a complete and strict relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions. J.E.L. codes: C72, D44.

One aspect of brainstorming that has received little research attention is how the brainstorming task should be presented to the group, whether as one allencompassing question or as a series of separate questions each focusing on one aspect of the task. This paper reports the results of an experiment in which groups electronically brainstormed on intact tasks (where all parts of the task were p...

In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab [1] configuration framework.

The idea of evolving novel rather than fit solutions has recently been offered as a way to automatically discover the kind of complex solutions that exhibit truly intelligent behavior. So far, novelty search has only been studied in the context of problems where the number of possible “different” solutions has been limited. In this paper, we show, using a task with a much larger solution space,...

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...

Demonstrating quantum computational advantage with strong hardness guarantees is shown to be possible using fermionic linear optics magic input states, and an experimentally feasible setup proposed.