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93
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 520 (40 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route t ..."
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Cited by 516 (27 self)
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We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimumlatency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Path Kernels and Multiplicative Updates
 Journal of Machine Learning Research
, 2003
"... Kernels are typically applied to linear algorithms whose weight vector is a linear combination of the feature vectors of the examples. Online versions of these algorithms are sometimes called "additive updates" because they add a multiple of the last feature vector to the current weight vector. ..."
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Cited by 61 (7 self)
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Kernels are typically applied to linear algorithms whose weight vector is a linear combination of the feature vectors of the examples. Online versions of these algorithms are sometimes called "additive updates" because they add a multiple of the last feature vector to the current weight vector.
Chromatic roots are dense in the whole complex plane
 In preparation
, 2000
"... to appear in Combinatorics, Probability and Computing I show that the zeros of the chromatic polynomials PG(q) for the generalized theta graphs Θ (s,p) are, taken together, dense in the whole complex plane with the possible exception of the disc q − 1  < 1. The same holds for their dichromatic pol ..."
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Cited by 37 (14 self)
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to appear in Combinatorics, Probability and Computing I show that the zeros of the chromatic polynomials PG(q) for the generalized theta graphs Θ (s,p) are, taken together, dense in the whole complex plane with the possible exception of the disc q − 1  < 1. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Pottsmodel partition functions) ZG(q,v) outside the disc q + v  < v. An immediate corollary is that the chromatic roots of notnecessarilyplanar graphs are dense in the whole complex plane. The main technical tool in the proof of these results is the Beraha–Kahane–Weiss theorem on the limit sets of zeros for certain sequences of analytic functions, for which I give a new and simpler proof. KEY WORDS: Graph, chromatic polynomial, dichromatic polynomial, Whitney rank function, Tutte polynomial, Potts model, Fortuin–Kasteleyn representation,
Optimal Processor Assignment for a Class of Pipelined Computations
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... The availability of large scale multitasked parallel architectures introduces the following processor assignment problem: we are given a long sequence of data sets, each of which is to undergo processing by a collection of tasks whose intertask data dependencies form a seriesparallel partial order ..."
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Cited by 17 (0 self)
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The availability of large scale multitasked parallel architectures introduces the following processor assignment problem: we are given a long sequence of data sets, each of which is to undergo processing by a collection of tasks whose intertask data dependencies form a seriesparallel partial order. Each individual task is potentially parallelizable, with a known experimentally determined execution signature. Recognizing that data sets can be pipelined through the task structure, the problem is to find a "good" assignment of processors to tasks. Two objectives interest us: minimal response time per data set given a throughput requirement, and maximal throughput given a response time requirement. Our approach is to decompose a seriesparallel task system into its essential "serial" and "parallel" components; our problem admits the independent solution and recomposition of each such component. We provide algorithms for the series analysis, and use an algorithm due to Krishnamurti and Ma...
Optimal Processor Assignment for Pipeline Computations
 IEEE TRANS. ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1994
"... The availability of largescale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual response times for different processor siz ..."
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Cited by 16 (7 self)
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The availability of largescale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual response times for different processor sizes, find an assignment of processors to tasks. Two objectives interest us: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, we assume that a large number of processors are to be assigned to a relatively small number of tasks. In this paper we develop efficient assignment algorithms for different classes of task structures. For a p processor system and a seriesparallel precedence graph with n constituent tasks, we provide an O(np2) algorithm that find the optimal assignment for the response time optimization problem; we find the assignment optimizing the constrained throughput in O(np2logp)time. Special cases of linear, independent, and tree graphs are also considered. In addition, we also examine more efficient algorithms when certain restrictions are placed on the problem parameters. Our techniques are applied to a task system in computer vision.
Parallel Recognition of SeriesParallel Graphs
, 1992
"... Recently, He and Yesha gave an algorithm for recognizing directed series parallel graphs, in time O(log 2 n) with linearly many EREW processors. We give a new algorithm for this problem, based on a structural characterization of series parallel graphs in terms of their ear decompositions. Our ..."
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Cited by 15 (1 self)
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Recently, He and Yesha gave an algorithm for recognizing directed series parallel graphs, in time O(log 2 n) with linearly many EREW processors. We give a new algorithm for this problem, based on a structural characterization of series parallel graphs in terms of their ear decompositions. Our algorithm can recognize undirected as well as directed series parallel graphs. It can be implemented in the CRCW model of parallel computation to take time O(log n). In the EREW model the time is O(log 2 n) but the number of processors required improves the bounds of the previous algorithm. 1 Introduction A directed graph G is twoterminal series parallel, with terminals s and t, if it can be produced by a sequence of the following operations: 1. Create a new graph, consisting of a single edge directed from s to t. 2. Given two twoterminal series parallel graphs X and Y , with terminals s X , t X , s Y , and t Y , form a new graph G = P (X,Y ) by identifying s = s X = s Y and t = ...
Optimal reduction of twoterminal directed acyclic graphs
 SIAM Journal on Computing
, 1992
"... Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O ..."
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Cited by 14 (1 self)
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Abstract. Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NPhard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly seriesparallel.