We consider the problem of designing a transportation network to allow the residents of the network to avail service provided by a single facility whose location is predetermined. This problem is known to be NPComplete for general graph. The problem remains NPComplete even when the vertices of the network are required to lie on the boundary of a convex polygon in the Euclidean plane. We present...

The consensus tree problem primarily arises in the domain of phylogenetics and seeks to find for a given collection of trees a single tree best representing it. Such a tree collection is usually obtained by biologists for a specific taxa set either via different phylogenetic inference methods or multiple applications of a nondeterministic procedure. Existing consensus methods often have the dis...

Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width 2. In this paper, we propose bounded vertex cover number Bayesian ...

Let G be an edge-colored graph. A tree T in G is a proper tree if no two adjacent edges of it are assigned the same color. Let k be a fixed integer with 2 ≤ k ≤ n. For a vertex subset S ⊆ V (G) with |S| ≥ 2, a tree is called an S-tree if it connects the vertices of S in G. A k-proper coloring of G is an edge-coloring of G having the property that for every set S of k vertices of G, there exists...

Recent studies on extractive text summarization formulate it as a combinatorial optimization problem such as a Knapsack Problem, a Maximum Coverage Problem or a Budgeted Median Problem. These methods successfully improved summarization quality, but they did not consider the rhetorical relations between the textual units of a source document. Thus, summaries generated by these methods may lack l...

Trees are a common structure to represent the inter-task communication pattern of a parallel algorithm. In this paper, we consider the embedding a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop two embeddings: i) a congestion-free, dilation-2, load-1 embedding of a level-p binary tree, and ii) a congestion-free, dilation-2, load-2 k emb...

The classic algorithm of Bodlaender and Kloks [J. Algorithms, 1996] solves the following problem in linear fixed-parameter time: given a tree decomposition of a graph of (possibly suboptimal) width k, compute an optimum-width tree decomposition of the graph. In this work, we prove that this problem can also be solved in mso in the following sense: for every positive integer k, there is an mso t...

The purpose of this paper is to show that a well known machine learning technique based on Decision Trees can be effectively used to select the best approach (in terms of efficiency) in an algorithm portfolio for a particular case study: the Bid Evaluation Problem (BEP) in Combinatorial Auctions. In particular, we are interested in deciding when to use a Constraint Programming (CP) approach and...

D u r i n g t h e l a s t few y e a r s t h e r e i s v i g o r o u s activity In constructing highly constrained grammatical systems by eliminating the transformational component either totally or partially. There is increasing recognition of t he f a c t t h a t the e n t i r e r a n g e o f d e p e n d e n c i e s t h a t t r a n s f o r m a t i o n a l g r a m m a r s i n t h e i r v a r i ...

Let A be a nonnegative real matrix which is expanding, i.e. all eigenvalues jj > 1. Suppose that j det(A)j is an integer and let D consists of exactly j det(A)j nonnegative vectors in R n. We classify all pairs (A; D) such that all x in the orthant R n + have at least one radix expansion using base A and digits in D. The matrix A must be a diagonal matrix times a permutation matrix. Also A must...