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Dynamic Graph Algorithms
, 1999
"... Introduction In many applications of graph algorithms, including communication networks, graphics, assembly planning, and VLSI design, graphs are subject to discrete changes, such as additions or deletions of edges or vertices. In the last decade there has been a growing interest in such dynamicall ..."
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Cited by 66 (1 self)
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Introduction In many applications of graph algorithms, including communication networks, graphics, assembly planning, and VLSI design, graphs are subject to discrete changes, such as additions or deletions of edges or vertices. In the last decade there has been a growing interest in such dynamically changing graphs, and a whole body of algorithms and data structures for dynamic graphs has been discovered. This chapter is intended as an overview of this field. In a typical dynamic graph problem one would like to answer queries on graphs that are undergoing a sequence of updates, for instance, insertions and deletions of edges and vertices. The goal of a dynamic graph algorithm is to update efficiently the solution of a problem after dynamic changes, rather than having to recompute it from scratch each time. Given their powerful versatility, it is not surprising that dynamic algorithms and dynamic data structures are often more difficult to design and analyze than their static c
Experimental analysis of dynamic all pairs shortest path algorithms
 In Proceedings of the fifteenth annual ACMSIAM symposium on Discrete algorithms
, 2004
"... We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to stat ..."
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Cited by 51 (5 self)
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We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to static algorithms on random, realworld and hard instances. Our experimental data suggest that some of the dynamic algorithms and their algorithmic techniques can be really of practical value in many situations. 1
Experimental Analysis of Dynamic Algorithms for the Single Source Shortest Path Problem
 ACM Jounal of Experimental Algorithmics
, 1997
"... In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bound ..."
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Cited by 27 (3 self)
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In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [31] and by Frigioni, MarchettiSpaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem; (b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the "asymptotic" behavior of algorithms, we also develope experiments by considering a widely used graph from the real world, i.e., the Internet graph. Work partially supported by the ESPRIT Long Term Research Project...
Decremental Dynamic Connectivity
 In Proceedings of the 8th ACMSIAM Symposium on Discrete Algorithms (SODA
, 1997
"... We consider Las Vegas randomized dynamic algorithms for online connectivity problems with deletions only. In particular, we show that starting from a graph with m edges and n nodes, we can maintain a spanning forest during m deletions in O(minfn 2 ; m log ng+ p nm log 2:5 n) expected total ti ..."
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Cited by 19 (1 self)
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We consider Las Vegas randomized dynamic algorithms for online connectivity problems with deletions only. In particular, we show that starting from a graph with m edges and n nodes, we can maintain a spanning forest during m deletions in O(minfn 2 ; m log ng+ p nm log 2:5 n) expected total time. This is amortized constant time per operation if we start with a complete graph. The deletions may be interspersed with connectivity queries, each of which is answered in constant time. The previous best bound was O(m log 2 n) by Henzinger and Thorup (1996), which covered both insertions and deletions. Our bound is stronger for m=n = !(log n). The result is based on a general randomized reduction of many deletionsonly queries to few deletions and insertions queries. Similar results are thus derived for 2edgeconnectivity, bipartiteness, and qweights minimum spanning tree. For the decremental dynamic kedgeconnectivity problem of deleting the edges of a graph starting with m edges ...
Experimental Analysis of Dynamic Minimum Spanning Tree Algorithms (Extended Abstract)
, 1997
"... ) Giuseppe Amato Giuseppe Cattaneo y Giuseppe F. Italiano z Abstract We conduct an extensive empirical study on the performance of several algorithms for maintaining the minimum spanning tree of a dynamic graph. In particular, we implemented and tested Frederickson's algorithms, and spa ..."
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Cited by 15 (2 self)
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) Giuseppe Amato Giuseppe Cattaneo y Giuseppe F. Italiano z Abstract We conduct an extensive empirical study on the performance of several algorithms for maintaining the minimum spanning tree of a dynamic graph. In particular, we implemented and tested Frederickson's algorithms, and sparsification on top of Frederickson's algorithms, and compared them to other dynamic algorithms. Moreover, we propose a variant of a dynamic algorithm by Frederickson, which was in our experience always faster than the other implementations derived from the papers. In our experiments, we considered both random and nonrandom inputs, with nonrandom inputs trying to enforce bad update patterns on the algorithms. For random inputs, a simple adaptation of a partially dynamic data structure on Kruskal's algorithm was the fastest implementation. For nonrandom inputs, sparsification yielded the fastest algorithm. In both cases, the performance of our variant of the algorithm of Frederickson was clos...
Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study
 In Proc. Workshop on Algorithm Engineering
, 2000
"... We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus ..."
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Cited by 12 (2 self)
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We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worstcase bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets. 1
Dynamically Switching Vertices in Planar Graphs
 ALGORITHMICA
, 2000
"... We consider graphs whose vertices may be in one of two different states: either on or off. We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off, and may insert a new edge or ..."
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Cited by 9 (0 self)
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We consider graphs whose vertices may be in one of two different states: either on or off. We wish to maintain dynamically such graphs under an intermixed sequence of updates and queries. An update may reverse the status of a vertex, by switching it either on or off, and may insert a new edge or delete an existing edge. A query tests whether any two given vertices are connected in the subgraph induced by the vertices that are on. We give efficient algorithms that maintain information about connectivity on planar graphs in O(log³ n) amortized time per query, insert, delete, switchon and switchoff operation over sequences of at least\Omega\Gamma n) operations, where n is the number of vertices of the graph.
An Experimental Study of Dynamic Algorithms for Transitive Closure
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2000
"... We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algori ..."
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Cited by 9 (2 self)
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We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algorithms as well as a new variant of them, both of which were always faster than any of the other implementations of the dynamic algorithms. We also considered simpleminded algorithms that were easy to implement and likely to be fast in practice. We tested and compared the above implementations on random inputs, on nonrandom inputs that are worstcase inputs for the dynamic algorithms, and on an input motivated by a realworld graph.
Shortest path tree computation in dynamic graphs
 IEEE Trans. Computers
, 2009
"... Let G = (V,E,w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G ′ be obtained from G by an application of a set of edge weight updates to G. Let s ∈ V, and let Ts and T ′s be Shortest Path Trees (SPTs) rooted at s in G and G′, respectively. The Dynamic Shortest Pa ..."
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Cited by 8 (0 self)
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Let G = (V,E,w) be a simple digraph, in which all edge weights are nonnegative real numbers. Let G ′ be obtained from G by an application of a set of edge weight updates to G. Let s ∈ V, and let Ts and T ′s be Shortest Path Trees (SPTs) rooted at s in G and G′, respectively. The Dynamic Shortest Path (DSP) problem is to compute T ′s from Ts. Existing work on this problem either focuses on a single edge weight change, or for multiple edge weight changes, some of them are incorrect or are not optimized. We correct and extend a few stateoftheart dynamic SPT algorithms to handle multiple edge weight updates. We prove that these algorithms are correct. Dynamic algorithms may not outperform static algorithms all the time. To evaluate the proposed dynamic algorithms, we compare them with the wellknown static Dijkstra’s algorithm. Extensive experiments are conducted with both reallife and artificial data sets. The experimental results suggest the most appropriate algorithms to be used under different circumstances.
A Software Library of Dynamic Graph Algorithms
, 1998
"... We report on a software library of dynamic graph algorithms. It was written in C++ as an extension of LEDA, the library of efficient data types and algorithms. It contains implementations of simple data structures as well as of sophisticated data structures for dynamic connectivity, dynamic minimum ..."
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Cited by 6 (2 self)
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We report on a software library of dynamic graph algorithms. It was written in C++ as an extension of LEDA, the library of efficient data types and algorithms. It contains implementations of simple data structures as well as of sophisticated data structures for dynamic connectivity, dynamic minimum spanning trees, dynamic single source shortest paths, and dynamic transitive closure. All data structures are implemented by classes derived from a common base class, thus they have a common interface. Additionally, the base class is in charge of keeping all dynamic data structures working on the same graph consistent. It is possible to change the structure of a graph by a procedure which is not aware of the dynamic data structures initialized for this graph. The library is easily extendible. 1 Introduction Traditional graph algorithms operate on static graphs. A fixed graph is given, and an algorithmic problem (e.g., "Is the graph planar?") is solved on the graph. Dynamic graphs are not fi...