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...

In this paper we de1ne the vertex-cover polynomial (G; ) for a graph G. The coe2cient of r in this polynomial is the number of vertex covers V ′ of G with |V ′|= r. We develop a method to calculate (G; ). Motivated by a problem in biological systematics, we also consider the mappings f from {1; 2; : : : ; m} into the vertex set V (G) of a graph G, subject to f−1(x) ∪ f−1(y) = ∅ for every edge x...

A graph G has a planar cover if there exists a planar graph H , and a homomorphism φ : H → G that maps the neighbours of each vertex bijectively. Each graph that has an embedding in the projective plane also has a finite planar cover. Negami conjectured the converse in 1988. This conjecture holds as long as no minor-minimal non-projective graph has a finite planar cover. From the list there rem...

A subset S of vertices of a graph G = (V,E) is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G and form a sequence ψ(G) = (ψ1(G), ψ2(G), . . . , ψ|V |(G)), called the path sequence of G. In this paper we prove necessary and sufficient conditions for two integers to appear on ...

We give an O(n) algorithm to find a minimum clique cover of a (bull, C4)-free graph, or equivalently, a minimum colouring of a (bull, 2K2)-free graph, where n is the number of vertices of the graphs.

In the course of history, a large number of politicians have been assassinated. To investigate this phenomenon, rational choice hypotheses are developed and tested using a large data set covering close to 100 countries over a period of 20 years. Several strategies, in addition to security measures, are shown to significantly reduce the probability of politicians being attacked or killed: extend...