Minimum Cycle Bases for Network Graphs

Berger, Franziska; Gritzmann, Peter; Vries, Sven de

doi:10.1007/s00453-004-1098-x

Cited by 66 publications

(61 citation statements)

References 11 publications

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“…However, even on the exact same graph, the addition of weights changes the performance substantially. This change in performance is not due to the difference in size of the produced Horton of an O(m 3 + mn 2 log n) algorithm described in [8].…”

Section: Running Timementioning

confidence: 97%

“…Except for Algorithms 1 (DP) and 2 (HYB) we include in the of an O(m 3 ) algorithm described in [8]. [8]. Algorithms 1 and 2 are implemented with compressed integer sets.…”

Section: Running Timementioning

confidence: 99%

“…It is presently known [7] that ω < 2.376. Recently Berger et al [8] gave another O(m 3 + mn 2 log n) algorithm by using similar ideas as de Pina. Finally, Kavitha et al [2] improved de Pina's algorithm into O(m 2 n+mn 2 log n) again by using fast matrix multiplication.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting algorithm seems to be very efficient in practice for random dense unweighted graphs. Finally, we compare our implementations with previous implementations of minimum cycle basis algorithms [3,8].…”

Section: Introductionmentioning

confidence: 99%

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Implementing Minimum Cycle Basis Algorithms

Mehlhorn

Michail

2005

Experimental and Efficient Algorithms

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Abstract. In this paper we consider the problem of computing a minimum cycle basis of an undirected graph G = (V, E) with n vertices and m edges. We describe an efficient implementation of an O(m 3 + mn 2 log n) algorithm presented in [1]. For sparse graphs this is the currently best known algorithm. This algorithm's running time can be partitioned into two parts with time O(m 3 ) and O(m 2 n + mn 2 log n) respectively. Our experimental findings imply that the true bottleneck of a sophisticated implementation is the O(m 2 n + mn 2 log n) part. A straightforward implementation would require Ω(nm) shortest path computations, thus we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speedup. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis used in [1,2] and [3,4], to obtain a new hybrid algorithm with running time O(m 2 n 2 ). The hybrid algorithm is very efficient in practice for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis in an undirected graph.

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Section: Running Timementioning

confidence: 97%

“…Except for Algorithms 1 (DP) and 2 (HYB) we include in the of an O(m 3 ) algorithm described in [8]. [8]. Algorithms 1 and 2 are implemented with compressed integer sets.…”

Section: Running Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implementing Minimum Cycle Basis Algorithms

Mehlhorn

Michail

2005

Experimental and Efficient Algorithms

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show abstract

“…Except for Algorithms 1 (DP) and 2 (HYB) we include in the [8]. Algorithms 1 and 2 are implemented with compressed integer sets.…”

Section: Running Timementioning

confidence: 99%

Implementing minimum cycle basis algorithms

Mehlhorn

Michail

2007

ACM J. Exp. Algorithmics

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Resilient Recursive Routing in Communication Networks

Nayak

2007

Handbook of Applied Algorithms

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The function of routing in communication networks is to determine a consistent set of local switching decisions at all the nodes such that data can be transported from any source to any destination. In general, routing algorithms can be loosely classified in many ways, for example, unicast versus multicast, centralized versus distributed, proactive versus reactive, single-path versus multipath, and so on, but in practice, routing algorithms can fall in between such simplistic classifications whose discussion is beyond the scope of this chapter. Furthermore, routing is frequently cast as an optimization problem, which can be either static or dynamic in nature (although in some instances routing can and is formulated as a constraint satisfaction problem).This chapter will concentrate on a dynamic, unicast, proactive, link-state routing algorithm only. The aim of the algorithm is to achieve a scalable approach to the representation and exploitation of path diversity in communication networks. By "scalable" we here mean that the number of message updates needed to support adaptation to changes in the state of the network scales well (i.e., as a polynomial) with respect to the number of nodes and links in the network. After a brief critique of wellestablished routing algorithms and their application to communication networks, we discuss the desirable properties of adaptive routing protocols. We then introduce a graph-theoretic framework on which a dynamic routing protocol can be constructed in a scalable fashion. This framework is a recursive abstraction of the physical network topology that can be also employed in analyzing the network path diversity, as well as the applicability of various types of dynamic routing protocols to a network belonging to a specific topology class. Finally, we present our routing protocol, called resilient recursive routing, which is built upon this framework, and demonstrate through simulations that it meets the desirable properties of adaptive routing protocols identified earlier.

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Minimum Cycle Bases for Network Graphs

Cited by 66 publications

References 11 publications

Implementing Minimum Cycle Basis Algorithms

Implementing Minimum Cycle Basis Algorithms

Implementing minimum cycle basis algorithms

Resilient Recursive Routing in Communication Networks

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