This paper studies the resolution of (augmented) weighted matching problems within a constraint programming framework. The first contribution of the paper is a set of branch-and-bound techniques that improves substantially the performance of algorithms based on constraint propagation and the second contribution is the introduction of weighted matching as a global constraint (MinWeightAllDifferent), that can be propagated using specialized incremental algorithms from Operations Research. We first compare programming techniques that use constraint propagation with specialized algorithms from Operations Research, such as the Busaker and Gowen flow algorithm or the Hungarian method. Although CLP is shown not to be competitive with specialized polynomial algorithms for "pure" matching problems, the situation is different as soon as the problems are modified with additional constraints. Using the previously mentioned set of techniques, a simpler branch-andbound algorithm based on constraint ...

A synchronous circuit built of functional elements and registers is a simple implementation of the semisystolic model of computation that can be used to design parallel algorithms. Retiming is a well-known technique that transforms a given circuit into a faster circuit by relocating its registers. We give tight bounds on the minimum clock period that can be achieved by retiming a synchronous circuit. These bounds are expressed in terms of the maximum delay-to-register ratio of the cycles in the circuit graph and the maximum propagation delay d max of the circuit components. Our bounds do not depend on the size of the circuit, and they are of theoretical as well as practical interest. They characterize exactly the minimum clock period that can be achieved by retiming a unit-delay circuit, and they lead to more efficient algorithms for several important problems related to retiming. Specifically, we give an O(V 1=2 E lg V ) algorithm for minimum clock period retiming of unitdelay circu...

ABSTRACT Constructing evolutionary trees for species sets is a fundamental problem in biology. Unfortunately, there is no single agreed upon method for this task, and many methods are in use. Current practice dictates that trees be constructed using different methods and that the resulting trees then be compared for consensus. It has become necessary to automate this process as the number of species under consideration has grown. We study the Unrooted Maximum Agreement Subtree Problem (UMAST) and its rooted variant (RMAST).

Software pipelining is one of the most important loop scheduling methods used by parallelizing compilers. It determines a static parallel schedule -- a periodic pattern -- to overlap instructions of a loop body from different iterations. The main contributions of this paper are the following: First, we propose to express the fine-grain loop scheduling problem (in particular, software pipelining) on the basis of the mathematical formulation of r-periodic scheduling. This formulation overcomes some of the problems encountered by existing software pipelining methods. Second, we demonstrate the feasibility of the proposed method by (1) presenting a polynomial time algorithm to find an optimal schedule in this r-periodic form that maximizes the computation rate (in fact, we show that this schedule maximizes the computation rate theoretically possible), and by (2) establishing polynomial bounds for the optimal schedule, i.e. bounds on its period, its periodicity, the pattern size, and the c...

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of e-complementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the e-relaxation algorithm for the minimum-cost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement e-relaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.

The cost scaling push-relabel method has been shown to be efficient for solving minimum-cost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.

Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Taijan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (uncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the

We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover.

We present a new all-pairs shortest path algorithm that works with real-weighted graphs in the traditional comparison-addition model. It runs in O(mn+n time, improving on the long-standing bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Here m and n are the number of edges and vertices, respectively.

Abstract. We study Pareto optimal matchings in the context of house allocation problems. We present an O ( √ nm) algorithm, based on Gale’s Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching. 1