In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and bounded number of terminals.

Given a graph G = (V, E) with a length function on edges and a subset R of V , the full Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the full Steiner tree problem is to find a full Steiner tree in G with minimum length, and the bottleneck full Steiner tree problem is to find a full Steiner tree T in G such that the length of the largest edge i...

Weextend an hypergraph representation, introducedby Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming (Energy minimization, partition function, base-pair probabilities. . . ) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one t...

We present a continuous, bilinear formulation for the fixed charge network flow problem. This formulation is used to derive an exact algorithm for the fixed charge network flow problem converging in a finite number of steps. Some preliminary computational experiments are reported to show the performance of the algorithm.

In this article we first review previous integer formulations for the maximum diversity problem. This problem consists of selecting a subset of elements from a data set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and expressions for upper bounds for this problem. As far as we know, this is the first exact algorith...

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by other columns that correspond to irreducible solutions of certain linear diophantine inequalities. We prove that various versions of our algorithm are finite. It is a major conc...

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P1 and P2 such that the sum of the perimeters of ch(P1) and ch(P2) is minimized, where ch(Pi) denotes the convex hull of Pi. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n2) time algorithm. Despite considerable progress on related problems, no subquadratic time algo...

Understanding the gene expression is an important factor to cancer diagnosis. One target of this understanding is implementing cancer gene search and classification methods. However, cancer gene search and classification is a challenge in that there is no an obvious exact algorithm that can be implemented individually for various cancer cells. In this paper a research is conducted through the m...

In this work, we take the traditional notation of contrast sets and extend them to other data types, in particular time series and by extension, images. In the traditional sense, contrast-set mining identifies attributes, values and instances that differ significantly across groups, and helps user understand the differences between groups of data. We reformulate the notion of contrastsets for t...

Recent techniques increase the amount of our knowledge of interactions between proteins. To filter, interpret and organize this data, many authors have provided tools for querying patterns in the shape of paths or trees in Protein-Protein Interaction networks. In this paper, we propose an exact algorithm for querying graphs pattern based on dynamic programming and color-coding. We provide an im...