Let each vertex v of a graph G have a positive integer weight ω(v). Then a multicoloring of G is to assign each vertex v a set of ω(v) colors so that any pair of adjacent vertices receive disjoint sets of colors. A partial k-tree is a graph with tree-width bounded by a fixed constant k. This paper presents an algorithm which finds a multicoloring of any given partial k-tree G with the minimum n...

For a real number p ≥ 2, an integer k > 0 and a set of terminals X in the plane, the Euclidean power-p Steiner tree problem asks for a tree interconnecting X and at most k Steiner points such that the sum of the p-th powers of the edge lengths is minimised. We show that this problem is in the complexity subclass exp-APX (but not poly-APX) of NPO. We then demonstrate that the approximation algor...

This work studies the problem of optimally locating sensors for monitoring chemical processes, formally known as the sensor network design and upgrade problem. This problem is an integer programming problem and has been solved to global optimality only using tree search methods using depth-first strategy. In this article, we exploit certain cost properties of the different nodes in the tree to ...

Trees are a common structure to represent the inter-task communication pattern of a parallel algorithm. In this paper, we consider the problem of embedding a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop a congestion-free, dilation-2, load-1 embedding of a level-p binary tree into an n-dimensional star graph, where p = n i=2 blog ic an...

A bstract-A new balanced multidimensional tree structure called a k-dimensional balanced binary tree, k a positive integer, is presented and investigated. It is shown that the data structure can be used to manage a set of n k-dimensional data items such that access, insertion, and deletion operations can be supported in Ooog n + k) time. The data structure is a multidimensional generalization o...

Consider the nearest neighbor graph for the integer lattice Z in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of spanning graphs for Z. This is shown to be a tree if and only if d ≤ 4. In this case, the tree has...

In the minimum-cost k-hop spanning tree (k-hop MST) problem, we are given a set S of n points in a metric space, a positive small integer k and a root point r ∈ S. We are interested in computing a rooted spanning tree of minimum cost such that the longest root-leaf path in the tree has at most k edges. We present a polynomial-time approximation scheme for the plane. Our algorithm is based on Ar...

ÐHigh-speed multiplication is frequently used in general-purpose and application-specific computer systems. These systems often support integer multiplication, where two n-bit integers are multiplied to produce a 2n-bit product. To prevent growth in word length, processors typically return the n least significant bits of the product and a flag that indicates whether or not overflow has occurred...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Problems with solutions based upon integer computations are collectively referred to as integer problems. Such problems occur routinely in pattern recognition, image processing, graph theory, and query processing. The purpose of this paper is to present constant time algorithms for computing the prefix sums of an integer sequence, and for solving the packing problem on reconfigurable meshes. Th...