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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 80 (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
Generalized submodular cover problems and applications
 Theoretical Computer Science
"... The greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to NPhard problems under certain conditions. The problems for which these conditions hold are known as submodular cover problems. The current paper 1 extends the applicability of the greedy ap ..."
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Cited by 35 (13 self)
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The greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to NPhard problems under certain conditions. The problems for which these conditions hold are known as submodular cover problems. The current paper 1 extends the applicability of the greedy approach to wider classes of problems. The usefulness of our extensions is illustrated by giving new approximate solutions for two dierent types of problems. The rst problem is that of nding the spanning tree of minimum weight among those whose diameter is bounded by D. A logarithmic ratio approximation algorithm is given for the cases of D = 4 and D = 5. This approximation ratio is also proved to be the best possible, unless P = NP. The second type involves some (known and new) center selection problems, for which new logarithmic ratio approximation algorithms are given. Again, it is shown that the ratio must be at least logarithmic unless P = NP.
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 appr ..."
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Cited by 31 (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 ...
Improved approximation algorithms for MinMax Tree Cover, Bounded Tree Cover, ShallowLight and BuyatBulk kSteiner Tree, and (k, 2)Subgraph
, 2011
"... 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 ..."
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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