Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). Using a variety of benchmark and random problems, we show that our bounds consistency algorithm is competitive with and can dramatically outperform existing state-of-the-art commercial implementations of constraint propagators for the gcc. We also present a new algorithm for domain consistency propagation of the gcc which improves on the worst-case performance of the best previous algorithm for problems that occur often in applications.

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Abstract. In this note, the problem of determining disjoint matchings in a set of intervals is investigated (two intervals can be matched if they are disjoint). Such problems find applications in schedules planning. First, we propose a new incremental algorithm to compute maximum disjoint matchings among intervals. We show that this algorithm runs in O(n) time if the intervals are given ordered in input. Additionally, a shorter algorithm is given for the case where the intervals are proper. Then, a N P-complete extension of this problem is considered: the perfect disjoint multidimensional matching problem among intervals. A sufficient condition is established for the existence of such a matching. The proof of this result yields a linear-time algorithm to compute it in this case. Besides, a greedy heuristic is shown to solve the problem in linear time for proper intervals. 1

The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application of the decomposition, we show an O(n) time and space algorithm for finding a longest path in a bipartite permutation graph.

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Claude-Guy Quimper ii We study in this thesis three well known global constraints. The All-Different constraint restricts a set of variables to be assigned to distinct values. The global cardinality constraint (GCC) ensures that a value v is assigned to at least lv vari-ables and to at most uv variables among a set of given variables where lv and uv are non-negative integers such that lv ≤ uv. The Inter-Distance constraint ensures that all variables, among a set of variables x1,..., xn, are pairwise distant from p, i.e. |xi − xj | ≥ p for all i � = j. The All-Different constraint, the GCC, and the Inter-Distance constraint are largely used in scheduling problems. For instance, in scheduling problems where tasks with unit processing time compete for a single

The greedy algorithm is a standard paradigm for solving matroid optimization problems on sequential computers. This paper presents a greedy algorithm suitable for a fully-pipelined linear array of processors, a generalization of Huang's algorithm [Hua90] for minimum spanning trees. Application of the algorithm to uniprocessor scheduling with release times and deadlines is discussed in detail. A key feature of the algorithm is its use of matroid contraction.

Parallel graph algorithm design is a very well studied topic. Many results have been presented for the PRAM model. However, these algorithms are inherently fine grained and experiments show that PRAM algorithms do often not achieve the expected speedup on real machines because of large message overheads. In this paper, we present coarse grained parallel graph algorithms with small message overheads that solve the following standard graph problems related to graph matching: finding maximum matchings in convex bipartite graphs, and finding maximum weight matchings in trees. To our knowledge, these are the first efficient parallel algorithms for these problems that are designed for standard commercial parallel machines such as off-the-shelf processor clusters. 1

A bipartite graph G = (V; W;E) is called convex if the vertices in W can be ordered in such a way that the elements of W adjacent to any vertex v 2 V form an interval (i.e. a sequence consecutively numbered vertices). Such a graph can be represented in a compact form that requires O(n) space, where n = maxfjV j; jW jg. Given a convex bipartite graph G in the compact form Dekel and Sahni designed an O(log 2 (n))-time, n-processor EREW PRAM algorithm to compute a maximum matching in G. We show that the matching produced by their algorithm can be used to construct optimally in parallel a maximum set of independent vertices. Our algorithm runs in O(logn) time with n=logn processors on a CRCW PRAM. Keywords: bipartite graphs, convex graphs, independent set, PRAM algorithms. 1. Introduction An independent set of a graph is a subset of its vertices such that no two vertices in the subset are adjacent. The problem of finding a maximum cardinality independent set (or shortly, the MIS prob...