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Linear Time 1/2Approximation Algorithm for Maximum Weighted Matching in General Graphs
 IN GENERAL GRAPHS, SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE, STACS 99
, 1998
"... A new approximation algorithm for maximum weighted matching in general edgeweighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(E), with E being the number of edges in the graph. T ..."
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Cited by 53 (0 self)
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A new approximation algorithm for maximum weighted matching in general edgeweighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(E), with E being the number of edges in the graph. This improves over the previously known 1/2approximation algorithms for maximum weighted matching which require O(E log(V)) steps, where V is the number of vertices.
Quality Matching and Local Improvement for Multilevel GraphPartitioning
, 1999
"... Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been ..."
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Cited by 31 (7 self)
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Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been proven on an experimental basis. In this paper we present new and efficient methods for both problems, while satisfying certain quality measurements. For the coarsening part we develop a new approximation algorithm for maximum weighted matching in general edgeweighted graphs. It calculates a matching with an edge weight of at least 1 2 of the edge weight of a maximum weighted matching. Its time complexity is O(jEj), with jEj being the number of edges in the graph. Furthermore, we use the HelpfulSet strategy for the local improvement of partitions. For partitioning graphs with a regular degree of 2k into 2 parts, it guarantees an upper bound of k\Gamma1 2 jV j + 1 on the cut size of th...
An Algorithm for Labeling Edges of Hierarchical Drawings
 Graph Drawing (Proc. GD '97), volume 1353 of Lecture Notes in Computer Science
, 1997
"... . Let G(V;E) be a graph, and let \Gamma be the drawing of G on the plane. We consider the problem of assigning text labels to every edge of G such that the quality of the label assignment is optimal. This problem has been first encountered in automated cartography. Even though much effort has been ..."
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Cited by 14 (3 self)
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. Let G(V;E) be a graph, and let \Gamma be the drawing of G on the plane. We consider the problem of assigning text labels to every edge of G such that the quality of the label assignment is optimal. This problem has been first encountered in automated cartography. Even though much effort has been devoted over the last 15 years in the area of automated drawing of maps, the Edge Label Placement (ELP) problem remains essentially unsolved. In this paper we investigate the ELP problem. We present an algorithm for the ELP problem more suitable for hierarchical drawings of graphs, but it can be adopted to many different drawing styles and still remain effective. Also, we present experimental results of our algorithm that indicate its effectiveness. 1 Introduction The area of graph drawing has grown significantly in the recent years motivated mostly by applications in information visualization [4, 17]. When visualizing information, it is essential to display not only the structure of the ob...
A Lower Bound for the Shortest Path Problem
"... We show that the Shortest Path Problem cannot be solved in o(log n) time on an unbounded fanin PRAM without bit operations using poly(n) processors even when the bitlengths of the weights on the edges are restricted to be of size O(log 3 n). This shows that the matrixbased repeated squaring al ..."
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Cited by 6 (0 self)
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We show that the Shortest Path Problem cannot be solved in o(log n) time on an unbounded fanin PRAM without bit operations using poly(n) processors even when the bitlengths of the weights on the edges are restricted to be of size O(log 3 n). This shows that the matrixbased repeated squaring algorithm for the Shortest Path Problem is optimal in the unbounded fanin PRAM model without bit operations. 1
Simple Competitive Request Scheduling Strategies
 in 11th ACM Symposium on Parallel Architectures and Algorithms
, 1999
"... In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Ev ..."
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Cited by 2 (0 self)
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In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Every request specifies two (distinct) resources and requires to get access to one of them. Furthermore, every request has a deadline of d, i.e. a request that arrives in round t has to be fulfilled during round t +d 1 at the latest. The number of requests which arrive during some round and the two alternative resources of every request are selected by an adversary. The goal is to maximize the number of requests that are fulfilled before their deadlines expire. We examine the scheduling problem in an online setting, i.e. new requests continuously arrive at the system, and we have to determine online an assignment of the requests to the resources in such a way that every resource has to fulfil...
Partitioning Graphs of Regular Degree
"... GraphPartitioning problems occur in a wide range of applications. The task is to divide the vertices of a graph in equally sized parts such that as few edges as possible are crossing the boundaries. The calculation of an optimal result is NPcomplete. We show a new strategy to derive upper bounds o ..."
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GraphPartitioning problems occur in a wide range of applications. The task is to divide the vertices of a graph in equally sized parts such that as few edges as possible are crossing the boundaries. The calculation of an optimal result is NPcomplete. We show a new strategy to derive upper bounds on the bisection width of graphs with regular degree. It gives optimal upper bounds for very small 3regular graphs and also the best known asymptotic upper bound for large 3regular graphs. The PARTY GraphPartitioning library includes several partitioning methods of different character. It has successfully been used in many applications and we will describe some of them. Lately, multilevel strategies are included to PARTY to allow an efficient partitioning of very large graphs. Especially fast matching algorithms which result in matchings with a high edge weight are used for this purpose. On this background, a new approximation algorithm for maximum weighted matching in general edgeweighte...