When BDDs are used for propagation in a constraint solver with nogood recording, it is necessary to find a small subset of a given set of variable assignments that is enough for a BDD to imply a new variable assignment. We show that the task of finding such a minimum subset is NP-complete by reduction from the hitting set problem. We present a new algorithm for finding such a minimal subset, wh...

Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, correspond...

In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that hits intersects all of them The problem is NP hard It is not known whether there exists a polynomial time approximation algorithm for the hitting set problem with a nite performance ratio Special cases of the hitting set problem are described for which nite performance ratios a...

This paper presents an O(1.2738 + kn)-time polynomialspace parameterized algorithm for Vertex Cover improving the previous O(1.286+kn)-time polynomial-space upper bound by Chen, Kanj, and Jia. The algorithm also improves the O(1.2745k+kn)-time exponentialspace upper bound for the problem by Chandran and Grandoni.

We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.

Model based diagnosis finds a growing range of practical applications, and significant performance-wise improvements have been achieved in recent years. Some of these improvements result from formulating the problem with maximum satisfiability (MaxSAT). Whereas recent work focuses on analyzing failing observations separately, it is also the case that in practical settings there may exist many f...

We address the problem of covering points with orthogonal polygons. Specifically, given a set of n grid-points in the plane each designated in advance with either a horizontal or vertical reading, we investigate the existence of an orthogonal polygon covering these n points in such a way that each edge of the polygon covers exactly one point and each point is covered by exactly one edge with th...

In popular music, a cover version or cover song, or simply cover, is a new performance or recording of a previously recorded, by someone other than the original artist. However, it is impossible to retrieve a piece of single track for most of people. Therefore, my goal is to deliver a program that separates a record into several tracks, each corresponding to a meaningful source, which can be us...

W e have had a good and active year here in Duke Physics: research groups are expanding, graduate recruitment was excellent, visibility increased both within and beyond campus, a new colloquium series has brought the department together more often, and we carried out the first phase of a reevaluation of our teaching of introductory physics. In this first section, I’ll touch on general issues th...