On applying the set covering model to reseeding

The Functional BIST approach is a rather new BIST technique based on exploiting embedded system functionality to generate deterministic test patterns during BIST. The approach takes advantages of two well-known testing techniques, the arithmetic BIST approach and the reseeding method. The main contribution of the present paper consists in formulating the problem of an optimal reseeding computation as an instance of the set covering problem. The proposed approach guarantees high flexibility, is applicable to different functional modules, and, in general, provides a more efficient test set encoding then previous techniques. In addition, the approach shorts the computation time and allows to better exploiting the tradeoff between area overhead and global test length as well as to deal with larger circuits

Variation In Greedy Approach To Set Covering Problem

The weighted set covering problem is to choose a number of subsets to cover all the elements in a universal set at the lowest cost. It is a well-studied classical problem with applications in various fields like machine learning, planning, information retrieval, facility allocation, etc. Deep web crawling refers to the process of gathering documents that have been structured into a data source and can be retrieved through a search interface. Its query selection process calls for an efficient solution to the set covering problem

The Covering Problem

An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a concrete objective to capture this understanding. In the literature, the standard choice for this objective is the membership problem, whose aim is to find a procedure deciding whether an input regular language can be defined in the logic under investigation. This approach was cemented as the right one by the seminal work of Sch\"utzenberger, McNaughton and Papert on first-order logic and has been in use since then. However, membership questions are hard: for several important fragments, researchers have failed in this endeavor despite decades of investigation. In view of recent results on one of the most famous open questions, namely the quantifier alternation hierarchy of first-order logic, an explanation may be that membership is too restrictive as a setting. These new results were indeed obtained by considering more general problems than membership, taking advantage of the increased flexibility of the enriched mathematical setting. This opens a promising research avenue and efforts have been devoted at identifying and solving such problems for natural fragments. Until now however, these problems have been ad hoc, most fragments relying on a specific one. A unique new problem replacing membership as the right one is still missing. The main contribution of this paper is a suitable candidate to play this role: the Covering Problem. We motivate this problem with 3 arguments. First, it admits an elementary set theoretic formulation, similar to membership. Second, we are able to reexplain or generalize all known results with this problem. Third, we develop a mathematical framework and a methodology tailored to the investigation of this problem

An Ant Colony based Hyper-Heuristic Approach for the Set Covering Problem

The Set Covering Problem (SCP) is a NP-hard combinatorial optimization problem that is challenging for meta-heuristic algorithms. In the optimization literature, several approaches using meta-heuristics have been developed to tackle the SCP and the quality of the results provided by these approaches highly depends on customized operators that demands high effort from researchers and practitioners. In order to alleviate the complexity of designing metaheuristics, a methodology called hyper-heuristic has emerged as a possible solution. A hyper-heuristic is capable of dynamically selecting simple low-level heuristics accordingly to their performance, alleviating the design complexity of the problem solver and obtaining satisfactory results at the same time. In a previous study, we proposed a hyper-heuristic approach based on Ant Colony Optimization (ACO-HH) for solving the SCP. This paper extends our previous efforts, presenting better results and a deeper analysis of ACO-HH parameters and behavior, specially about the selection of low-level heuristics. The paper also presents a comparison with an ACO meta-heuristic customized for the SCP

Covering Pairs in Directed Acyclic Graphs

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation sequencing technologies in bioinformatics. The first problem (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum cardinality set of paths "covering" all the vertices such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The second problem (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a path containing the maximum number of the given pairs of vertices. We show its NP-hardness and also its W[1]-hardness when parametrized by the number of covered pairs. On the positive side, we give a fixed-parameter algorithm when the parameter is the maximum overlapping degree, a natural parameter in the bioinformatics applications of the problem

A Local Search-Based Approach for Set Covering

In the Set Cover problem, we are given a set system with each set having a weight, and we want to find a collection of sets that cover the universe, whilst having low total weight. There are several approaches known (based on greedy approaches, relax-and-round, and dual-fitting) that achieve a $H_k \approx \ln k + O(1)$ approximation for this problem, where the size of each set is bounded by $k$. Moreover, getting a $\ln k - O(\ln \ln k)$ approximation is hard. Where does the truth lie? Can we close the gap between the upper and lower bounds? An improvement would be particularly interesting for small values of $k$, which are often used in reductions between Set Cover and other combinatorial optimization problems. We consider a non-oblivious local-search approach: to the best of our knowledge this gives the first $H_k$-approximation for Set Cover using an approach based on local-search. Our proof fits in one page, and gives a integrality gap result as well. Refining our approach by considering larger moves and an optimized potential function gives an $(H_k - \Omega(\log^2 k)/k)$-approximation, improving on the previous bound of $(H_k - \Omega(1/k^8))$ (\emph{R.\ Hassin and A.\ Levin, SICOMP '05}) based on a modified greedy algorithm.Comment: To appear in SOSA '2