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...

We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vector-valued — or Pareto — optima for collision-free coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key dist...

A terrain T is an x-monotone polygonal chain in the plane; T is orthogonal if each edge of T is either horizontal or vertical. In this paper, we give an exact algorithm for the problem of guarding the convex vertices of an orthogonal terrain with the minimum number of reflex vertices.

Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over Q(t1, t2, . . . , tm) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.

The queen graph coloring problem consists in covering a n × n chessboard with n queens, so that two queens of the same color cannot attack each other. When the size, n, of the chessboard is a multiple of 2 or 3, it is hard to color the queen graph with only n colors. We have developed an exact algorithm which is able to solve exhaustively this problem for dimensions up to n = 12 and find one so...

This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets d coupons each run and he chooses the one that he has the least so far. In the asymptotic case when the number of coupons n goes to infinity, we show that on average n log n d + n d (m−1) log log n+O(mn) runs are needed to collect m sets of coupons. An efficient exact algorithm is ...