Let G be an unweighted graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5. This is the first algorithm breaking the trivial n!-barrier.

Realization of efficient Universal Logic Modules (ULMs) is a challenging topic in circuit design. The goal is to find a representation that allows to realize as many Boolean functions as possible by permutation of inputs or phase assignment. In this paper an exact algorithm for finding a minimal circuit for a ULM is presented. The approach is parametrisized in several ways, e.g. the user can de...

In this paper we study a variant of the Capacitated Team Orienteering Problem (CTOP), that is the problem where a fleet of vehicles, each with a constraint on the time available, is given to serve profitable customers with the objective of maximizing the collected profit. We study the variant where customers may be only partially served (incomplete service) and, if beneficial, also by more than...

This paper presents an algorithm for comparing large numbers of traces to each other and identifying and presenting groups of traces with similar features. It is applied to forensic analysis in which groups of similar traces are automatically identified and presented so that attribution and other related claims may be asserted, and independently confirmed or refuted. The approach of this paper ...

Recent research on qualitative reasoning has focussed on representing and reasoning about events that occur repeatedly. Allen's interval algebra has been modiied to model events that are collections of convex intervals|a non-convex interval. Using the modiied version of Allen's algebra, constraint-based algorithms have been investigated for nding feasible relations in a network of non-convex in...

The primal-dual method increases the dual variables gradually until some dual constraint becomes tight. Then, the primal variable corresponding to the tight dual constraint is ‘bought’ (or selected), and the process continues till we get a feasible primal solution. Next, we compare the value of the primal solution to the value of the dual solution to get an appropriate approximation factor (or ...

In the Petrol Station Replenishment Problem (PSRP) the aim is to jointly determine an allocation of petroleum products to tank truck compartments and to design delivery routes to stations. This article describes an exact algorithm for the PSRP. This algorithm was extensively tested on randomly generated data and on a real-life case arising in Eastern Quebec.

Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once a...

Let V be a finite configuration of voter ideal points in the Euclidean plane. For given > 0 a point x ∈ < is in the -core if for all y 6= x, ||v−x|| ≤ ||v− y||+ for a simple majority (at least |V |/2) of voters v ∈ V . Let (x) denote the the least for which x is in the -core. Thus (x) = 0 if and only if x is a core point. The least for which the -core is nonempty is denoted ∗. This paper provid...