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A New Approach to Dynamic All Pairs Shortest Paths
, 2002
"... We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with nonnegative realvalued edge weights that supports any sequence of operatio ..."
Abstract

Cited by 73 (9 self)
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We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with nonnegative realvalued edge weights that supports any sequence of operations in e O(n amortized time per update and unit worstcase time per distance query, where n is the number of vertices. We can also report shortest paths in optimal worstcase time. These bounds improve substantially over previous results and solve a longstanding open problem. Our algorithm is deterministic and uses simple data structures.
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
 In IEEE Symposium on Foundations of Computer Science
, 2001
"... We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and que ..."
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Cited by 35 (10 self)
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We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with realvalued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and queries in optimal worstcase time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with onesided error which supports updates faster in O(S We also show how to obtain query/update tradeo#s for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of O(n/k), and improve over the best known update bounds for k in the . Algorithms in the second family achieve an update bound of ), and are competitive with the best known update bounds (first family included) for k in the range (n/S) # Work partially supported by the IST Programme of the EU under contract n. IST199914. 186 (ALCOMFT) and by CNR, the Italian National Research Council, under contract n. 01.00690.CT26. Portions of this work have been presented at the 42nd Annual Symp. on Foundations of Computer Science (FOCS 2001) [8] and at the 29th International Colloquium on Automata, Languages, and Programming (ICALP'02) [9].
A Practical Temporal Constraint Management System for RealTime Applications
"... Abstract. A temporal constraint management system (TCMS) is a temporal network together with algorithms for managing the constraints in that network over time. This paper presents a practical TCMS, called MYSYSTEM, that efficiently handles the propagation of the kinds of temporal constraints commonl ..."
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Cited by 3 (2 self)
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Abstract. A temporal constraint management system (TCMS) is a temporal network together with algorithms for managing the constraints in that network over time. This paper presents a practical TCMS, called MYSYSTEM, that efficiently handles the propagation of the kinds of temporal constraints commonly found in realtime applications, while providing constanttime access to “allpairs, shortestpath ” information that is extremely useful in many applications. The temporal network in MYSYSTEM includes special timepoints for dealing with the passage of time and eliminating the need for certain common forms of constraint propagation. The constraint propagation algorithm in MYSYSTEM maintains a restricted set of entries in the associated allpairs, shortestpath matrix by incrementally propagating changes to the network either from adding a new constraint or strengthening, weakening or deleting an existing constraint. The paper presents empirical evidence to support the claim that MYSYSTEM is scalable to realtime planning, scheduling and acting applications. 1
A Dynamic Data Structure for Maintaining Disjoint Paths Information in Digraphs
"... Abstract. In this paper we present the first dynamic data structure for testing in constant time the existence of two edge or quasiinternally vertexdisjoint paths p1 from s to t1 and p2 from s to t2 for any three given vertices s, t1, and t2 of a digraph. By quasiinternally vertexdisjoint we ..."
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Abstract. In this paper we present the first dynamic data structure for testing in constant time the existence of two edge or quasiinternally vertexdisjoint paths p1 from s to t1 and p2 from s to t2 for any three given vertices s, t1, and t2 of a digraph. By quasiinternally vertexdisjoint we mean that no inner vertex of p1 appears on p2 and vice versa. Moreover, for two vertices s and t, the data structure supports the output of all vertices and all edges whose removal would disconnect s and t in a time linear in the size of the output. The update operations consist of edge insertions and edge deletions, where the implementation of edge deletions will be given only in the full version of this paper. The update time after an edge deletion is competitive with the reconstruction of a static data structure for testing the existence of disjoint paths in constant time, whereas our data structure performs much better in the case of edge insertions. 1
Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
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This is the second annual progress report for the ALCOMFT project, supported by the European
A New Approach to Dynamic All Pairs . . .
 IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC’03
, 2003
"... We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with nonnegative realvalued edge weights that supports any sequence of opera ..."
Abstract
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We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with nonnegative realvalued edge weights that supports any sequence of operations in O(n time per update and unit worstcase time per distance query, where n is the number of vertices. We can also report shortest paths in optimal worstcase time. These bounds improve substantially over previous results and solve a longstanding open problem. Our