Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs

In the strongly connected spanning subgraph ([Formula: see text]) problem, the goal is to find a minimum weight spanning subgraph of a strongly connected directed graph that maintains the strong connectivity. In this paper, we consider the [Formula: see text] problem for two families of geometric directed graphs; [Formula: see text]-spanners and symmetric disk graphs. Given a constant [Formula: see text], a directed graph [Formula: see text] is a [Formula: see text]-spanner of a set of points [Formula: see text] if, for every two points [Formula: see text] and [Formula: see text] in [Formula: see text], there exists a directed path from [Formula: see text] to [Formula: see text] in [Formula: see text] of length at most [Formula: see text], where [Formula: see text] is the Euclidean distance between [Formula: see text] and [Formula: see text]. Given a set [Formula: see text] of points in the plane such that each point [Formula: see text] has a radius [Formula: see text], the symmetric disk graph of [Formula: see text] is a directed graph [Formula: see text], such that [Formula: see text]. Thus, if there exists a directed edge [Formula: see text], then [Formula: see text] exists as well. We present [Formula: see text] and [Formula: see text] approximation algorithms for the [Formula: see text] problem for [Formula: see text]-spanners and for symmetric disk graphs, respectively. Actually, our approach achieves a [Formula: see text]-approximation algorithm for all directed graphs satisfying the property that, for every two nodes [Formula: see text] and [Formula: see text], the ratio between the shortest paths, from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] in the graph, is at most [Formula: see text].

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THE EFFECT OF ASYMMETRY ON THE ON-LINE MULTICAST ROUTING PROBLEM

International Journal of Foundations of Computer Science ◽

10.1142/s0129054102001527 ◽

2002 ◽

Vol 13 (06) ◽

pp. 889-910 ◽

Cited By ~ 6

Author(s):

MICHALIS FALOUTSOS ◽

RAJESH PANKAJ ◽

KENNESTH C. SEVCIK

Keyword(s):

Greedy Algorithm ◽

Multicast Routing ◽

Directed Graphs ◽

Shortest Paths ◽

Worst Case ◽

Routing Problem ◽

On Line ◽

The Asymmetry ◽

The Greedy Algorithm

In this paper, we study the problem of multicast routing on directed graphs. We define the asymmetry of a graph to be the maximum ratio of weights on opposite directed edges between a pair of nodes for all node-pairs. We examine three types of problems according the membership behavior: (i) the static, (ii) the join-only, (iii) the join-leave problems. We study the effect of the asymmetry on the worst case performance of two algorithms: the Greedy and Shortest Paths algorithms. The worst case performance of Shortest Paths is poor, but it is affected by neither the asymmetry nor the membership behavior. In contrast, the worst case performance of Greedy is a proportional to the asymmetry in a some cases. We prove an interesting result for the join-only problem: the Greedy algorithm has near-optimal on-line performance.

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Automatic Dynamic Web Service Composition Using AND/OR Directed Graphs

International Journal of Web Services Research ◽

10.4018/ijwsr.2019070102 ◽

2019 ◽

Vol 16 (3) ◽

pp. 29-43

Author(s):

Hajar Elmaghraoui ◽

Laila Benhlima ◽

Dalila Chiadmi

Keyword(s):

Web Service ◽

Service Composition ◽

Directed Graphs ◽

Shortest Paths ◽

Web Service Composition ◽

Optimization Techniques ◽

Semantic Relationship ◽

Query Process ◽

Dynamic Web ◽

And Performance

In this article, the authors propose a dynamic web service composition approach based on representing the semantic relationship between web services using a weighted directed AND/OR graph. The nodes in this graph represent available services while the arcs represent the semantic input/output dependencies among them. The novelty of this work consists of constructing the graph and computing offline the shortest paths between each pair of its nodes to disconnect this tedious task from the composition query process. A set of dynamic optimization techniques has been included to reduce the size of the graph and thus improve the scalability and performance of this approach. In addition to the sequence and fork relations between services, this solution also supports the parallel relation. Furthermore, a recovery mechanism is integrated to ensure the continuity of the execution of the composition.

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Maintaining shortest paths under deletions in weighted directed graphs

Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13 ◽

10.1145/2488608.2488701 ◽

2013 ◽

Cited By ~ 17

Author(s):

Aaron Bernstein

Keyword(s):

Directed Graphs ◽

Shortest Paths

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Centrality and shortest path length measures for the functional analysis of urban drainage networks

Applied Network Science ◽

10.1007/s41109-019-0247-8 ◽

2020 ◽

Vol 5 (1) ◽

Author(s):

Julian D. Reyes-Silva ◽

Jonatan Zischg ◽

Christopher Klinkhamer ◽

P. Suresh C. Rao ◽

Robert Sitzenfrei ◽

...

Keyword(s):

Complex Dynamics ◽

Directed Graphs ◽

Shortest Paths ◽

Weighting Factor ◽

Urban Drainage ◽

Frequency Distributions ◽

Drainage Networks ◽

Flow Transport ◽

Topological Measures ◽

Highly Correlated

AbstractThe objective of this research is to evaluate whether complex dynamics of urban drainage networks (UDNs) can be expressed in terms of their structure, i.e. topological characteristics. The present study focuses on the application of topological measures for describing the transport and collection functions of UDNs, using eight subnetworks of the Dresden sewer network as study cases. All UDNs are considered as weighted directed graphs, where edge weights correspond to structural and hydraulic pipe characteristics which affect flow. Transport functions are evaluated in terms of travel time distributions (TTDs), under the hypothesis that frequency distributions of Single Destination Shortest Paths (SDSP) of nodes to the outlet had similar shapes than TTDs. Assessment of this hypothesis is done based on two-sample Kolmogorov-Smirnov tests and comparisons of statistical moments. Collection analysis, i.e. determination of flow paths, is done based on two approaches: (1) using Edge Betweenness Centrality (EBC), and (2) based on the number of SDSP going through an edge connecting a node to the outlet, referred as Paths. Hydrodynamic simulation results are used to validate the outcomes of graph analysis with actual flow behaviors. Results indicate that given an appropriate edge weighting factor, in this case Residence Time, SDSP has the potential to be used as an indicator for flow transport in UDNs. Moreover, both EBC and Paths values were highly correlated to average flows. The first approach, however, proved to be inadequate for estimating flows near the outlet but appropriate for identifying different paths in meshed systems, while the second approach lead to better results in branched networks. Further studies regarding the influence of UDNs layout are needed.

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