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Bicriteria network design problems
 In Proc. 22nd Int. Colloquium on Automata, Languages and Programming
, 1995
"... We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes ..."
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Cited by 76 (13 self)
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We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes the second objective subject to the budget on the first. We consider three different criteria the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomialtime approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same we present a “black box ” parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a clusterbased approach to devise a approximation algorithms — the solutions output violate
Approximating the Weight of Shallow Steiner Trees
 DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science
, 1998
"... This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of k vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d <= 5. Here we give a polynomial time approxi ..."
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Cited by 29 (3 self)
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This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of k vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d <= 5. Here we give a polynomial time approximation algorithm of ratio O(log k) for constant d, which is asymptotically optimal unless P = NP , and an algorithm of ratio O( k^{\epsilon})), for any fixed 0 < \epsilon < 1, for general d. Keywords: NPhard problems, approximation algorithms, Steiner trees 1 Introduction 1.1 The problem This paper considers the problem of finding low diameter Steiner trees of minimum weight. Given an nvertex graph G(V
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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Cited by 8 (0 self)
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NPcomplete for all values of k; 4 k (n  2), except when all edgeweights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree datastructure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomialtime algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter4 tree is also used for evaluating the quality of o...
Models of Bitmap Generation: A Systematic Approach to Bitmap Compression
 Inf. Proc. & Management, v28
, 1992
"... : In large IR systems, information about word occurrence may be stored in form of a bit matrix, with rows corresponding to different words and columns to documents. Such a matrix is generally very large and very sparse. New methods for compressing such matrices are presented, which exploit possible ..."
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Cited by 5 (2 self)
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: In large IR systems, information about word occurrence may be stored in form of a bit matrix, with rows corresponding to different words and columns to documents. Such a matrix is generally very large and very sparse. New methods for compressing such matrices are presented, which exploit possible correlations between rows and between columns. The methods are based on partitioning the matrix into small blocks and predicting the 1bit distribution within a block by means of various bit generation models. Each block is then encoded using Huffman or arithmetic coding. The methods also use a new way of enumerating subsets of fixed size from a given superset. Preliminary experimental results indicate improvements over previous methods. 1. Introduction The common approach to processing complex boolean queries in large fulltext document retrieval systems is to use inverted files: a concordance is accessed via a dictionary, and includes for each different word of the text, the ordered list ...
Computer Science is no more about computers than astronomy is about telescopes – E. W. Dijkstra. University of Alberta Improved approximation algorithms for MinMax Tree Cover, Bounded Tree Cover, ShallowLight and BuyatBulk kSteiner Tree, and (k, 2)S
"... Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of ..."
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Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission. To my mother In this thesis we provide improved approximation algorithms for the MinMax kTree Cover, Bounded Tree Cover and ShallowLight kSteiner Tree, (k, 2)subgraph problems. In Chapter 2 we consider the MinMax kTree Cover (MMkTC). Given a graph G = (V, E) with weights w: E → Z +, a set T1, T2,..., Tk of subtrees of G is called a tree cover of G if V = ⋃ k i=1 V (Ti). In the MMkTC problem we are given graph G and a positive integer