Boolean factor analysis aims at decomposing an objects × attributes Boolean matrix I into a Boolean product of an objects × factors Boolean matrix A and a factors × attributes Boolean matrix B, with the number of factors as small as possible. This paper is a continuation of our previous paper where we proved that formal concepts of I are optimal factors for Boolean factor analysis. In particula...

Recently, Chakrabarty et al. [5] initiated a systematic study of capacitated set cover problems, and considered the question of how their approximability relates to that of the uncapacitated problem on the same underlying set system. Here, we investigate this connection further and give several results, both positive and negative. In particular, we show that if the underlying set system satisfi...

We propose an effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique” is closely related to a tree-like set covering problem.

The DISCRETE edit system, based on the Fellegi and Holt model [1976] of editing, contains two major components: edit generation and error localization. The set covering problem (SCP) is formulated with constraint matrices many times in both components. Therefore, an e cient set covering algorithm is critical to the overall performance of the DISCRETE edit system. The design of a set covering al...

The rst contribution of this paper is a theoretical comparison of the (1+1)-EA evolutionary algorithm to other evolutionary algorithms in the case of so-called monotone reproduction operator, which indicates that the (1+1)-EA is an optimal search technique in this setting. After that we study the expected optimization time for the (1+1)-EA and show two set covering problem families where it is ...

The optimization of container ship and depot operations embeds the k-shift problem, in which containers must be stowed in stacks such that at most k containers must be removed in order to reach containers below them. We first solve an open problem introduced by Avriel et al. (2000) by showing that changing from uncapacitated to capacitated stacks reduces the complexity of this problem from NP-c...

Introduction It is often important to coordinate teams of cooperative agents in a distributed manner. We study how to assign tasks to cooperative agents so that the resulting team cost is small (that is, team performance is high). Market-based mechanisms are promising distributed task-allocation methods. Robotics researchers have recently studied how to use sequential single-item (SSI) auctions...

Abstract: In this paper, we develop a simultaneous column-and-row generation algorithm that could be applied to a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many to be...