Results 1  10
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65
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 140 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Packing Steiner trees
"... The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study this p ..."
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Cited by 88 (5 self)
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The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study this problem and present an algorithm with an asymptotic approximation factor of S/4. This gives a sufficient condition for the existence of k edgedisjoint Steiner trees in a graph in terms of the edgeconnectivity of the graph. We will show that this condition is the best possible if the number of terminals is 3. At the end, we consider the fractional version of this problem, and observe that it can be reduced to the minimum Steiner tree problem via the ellipsoid algorithm.
Web Usage Mining: Discovery and Application of Interestin Patterns from Web Data
, 2000
"... Web Usage Mining is the application of data mining techniques to Web clickstream data in order to extract usage patterns. As Web sites continue to grow in size and complexity, the results of Web Usage Mining have become critical for a number of applications such as Web site design, business and mark ..."
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Cited by 72 (0 self)
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Web Usage Mining is the application of data mining techniques to Web clickstream data in order to extract usage patterns. As Web sites continue to grow in size and complexity, the results of Web Usage Mining have become critical for a number of applications such as Web site design, business and marketing decision support, personalization, usability studies, and network trac analysis. The two major challenges involved in Web Usage Mining are preprocessing the raw data to provide an accurate picture of how a site is being used, and ltering the results of the various data mining algorithms in order to present only the rules and patterns that are potentially interesting. This thesis develops and tests an architecture and algorithms for performing Web Usage Mining. An evidence combination framework referred to as the information lter is developed to compare and combine usage, content, and structure information about a Web site. The information lter automatically identi es the discovered ...
SingleSource Unsplittable Flow
 In Proceedings of the 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The maxflow mincut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following singlesource disjoint paths problem: given a graph G, with a source vertex s and termin ..."
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Cited by 54 (2 self)
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The maxflow mincut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following singlesource disjoint paths problem: given a graph G, with a source vertex s and terminals t 1 , ..., t k , decide whether there exist edgedisjoint st i paths, for i = 1, ..., k. We consider a natural, NPhard generalization of this problem, which we call the singlesource unsplittable flow problem. We are given a source and terminals as before; but now each terminal t i has a demand ae i 1, and each edge e of G has a capacity c e 1. The problem is to decide whether one can choose a single st i path, for each i, so that the resulting set of paths respects the capacity constraints  the total amount of demand routed across any edge e must be bounded by the capacity c e . The main results of this paper are constantfactor approximation algorithms for three n...
An Approximation Algorithm for MinimumCost VertexConnectivity Problems
, 1997
"... We present an approximation algorithm for solving graph problems in which a lowcost set of edges must be selected that has certain vertexconnectivity properties. In the survivable network design problem, one is given a value r ij for each pair of vertices i and j, and must find a minimumcost set ..."
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Cited by 51 (7 self)
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We present an approximation algorithm for solving graph problems in which a lowcost set of edges must be selected that has certain vertexconnectivity properties. In the survivable network design problem, one is given a value r ij for each pair of vertices i and j, and must find a minimumcost set of edges such that there are r ij vertexdisjoint paths between vertices i and j. In the case for which r ij 2 f0; 1; 2g for all i; j, we can find a solution of cost no more than 3 times the optimal cost in polynomial time. In the case in which r ij = k for all i; j, we can find a solution of cost no more than 2H(k) times optimal, where H(n) = 1 + 1 2 + \Delta \Delta \Delta + 1 n . No approximation algorithms were previously known for these problems. Our algorithms rely on a primaldual approach which has recently led to approximation algorithms for many edgeconnectivity problems. 1 Introduction Let G = (V; E) be an undirected graph with nonnegative costs c e 0 on all edges e 2 E. In...
Connectivity and Inference Problems for Temporal Networks
 J. Comput. Syst. Sci
, 2000
"... Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. ..."
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Cited by 51 (3 self)
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Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated. ” We will call such a graph a temporal network. To model the notion that information in such a network “flows ” only on paths whose labels respect the ordering of time, we call a path timerespecting if the time labels on its edges are nondecreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on timerespecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the
Treewidth: Computational Experiments
, 2001
"... Many NPhard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost ..."
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Cited by 43 (12 self)
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Many NPhard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for fixed k, linear time algorithms exist to solve the decision problem “treewidth < k”, their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on wellknown algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary.
Network Coding Fundamentals
 FOUNDATIONS AND TRENDS IN NETWORKING
, 2007
"... Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new techni ..."
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Cited by 28 (7 self)
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Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new technique: how network coding works and what are its benefits, how network codes are designed and how much it costs to deploy networks implementing such codes, and finally, whether there are methods to deal with cycles and delay that are present in all real networks. A companion issue deals primarily with applications of network coding.
The encoding complexity of network coding
 Issue 6, June 2006, Page(s):2386
"... Abstract—In the multicast network coding problem, a source needs to deliver packets to a set of terminals over an underlying communication network. The nodes of the multicast network can be broadly categorized into two groups. The first group incudes encoding nodes, i.e., nodes that generate new pac ..."
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Cited by 23 (3 self)
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Abstract—In the multicast network coding problem, a source needs to deliver packets to a set of terminals over an underlying communication network. The nodes of the multicast network can be broadly categorized into two groups. The first group incudes encoding nodes, i.e., nodes that generate new packets by combining data received from two or more incoming links. The second group includes forwarding nodes that can only duplicate and forward the incoming packets. Encoding nodes are, in general, more expensive due to the need to equip them with encoding capabilities. In addition, encoding nodes incur delay and increase the overall complexity of the network. Accordingly, in this paper, we study the design of multicast coding networks with a limited number of encoding nodes. We prove that in a directed acyclic coding network, the number of encoding nodes required to achieve the capacity of the network is bounded by 3 2. Namely, we present (efficiently constructible) network codes that achieve capacity in which the total number of encoding nodes is independent of the size of the network and is bounded by 3 2. We show that the number of encoding nodes may depend both on and by presenting acyclic coding networks that require ( 2) encoding nodes. In the general case of coding networks with cycles, we show that the number of encoding nodes is limited by the size of the minimum feedback link set, i.e., the minimum number of links that must be removed from the network in order to eliminate cycles. We prove that the number of encoding nodes is bounded by (2 +1) 3 2, where is the minimum size of a feedback link set. Finally, we observe that determining or even crudely approximating the minimum number of required encoding nodes is anhard problem. Index Terms—Coding networks, encoding links, encoding nodes, multicast, network coding. I.
An Approximate MaxSteinerTreePacking MinSteinerCut Theorem
"... Given an undirected multigraph G and a subset of vertices S ` V (G), the STEINER TREE PACKING problem is to find a largest collection of edgedisjoint trees that each connects S. This problem and its generalizations have attracted considerable attention from researchers in different areas because of ..."
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Cited by 23 (4 self)
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Given an undirected multigraph G and a subset of vertices S ` V (G), the STEINER TREE PACKING problem is to find a largest collection of edgedisjoint trees that each connects S. This problem and its generalizations have attracted considerable attention from researchers in different areas because of their wide applicability. This problem was shown to be APXhard (no polynomial time approximation scheme unless P=NP). In fact, prior to this paper, not evenan approximation algorithm with asymptotic ratio o(n) wasknown despite several attempts. In this work, we close this huge gap by presenting the first polynomial time constant factor approximation algorithm for the STEINER TREE PACKING problem. The maintheorem is an approximate minmax relation between the maximum number of edgedisjoint trees that each connects S (i.e. Strees) and the minimum size of an edgecut thatdisconnects some pair of vertices in S (i.e. Scut). Specifically, we prove that if the minimum Scut in G has 26k edges, then G has at least k edgedisjoint Strees; this answers Kriesell's conjecture affirmatively up to a constant multiple. The techniques that we use are purely combinatorial, where matroid theory is the underlying ground work.