An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
Experimental analysis of dynamic algorithms for the single source shortest paths problem
Journal of Experimental Algorithmics (JEA)
An On-Line Edge-Deletion Problem
Journal of the ACM (JACM)
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Witnesses for Boolean matrix multiplication and for shortest paths
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Improved Distance Oracles for Avoiding Link-Failure
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Algorithms and theory of computation handbook
Delineating imprecise regions via shortest-path graphs
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
An experimental study of algorithms for fully dynamic transitive closure
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computers and Operations Research
Pay-as-you-go maintenance of precomputed nearest neighbors in large graphs
Proceedings of the 21st ACM international conference on Information and knowledge management
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We present a simple space saving trick that applies to many previous algorithms for transitive closure and shortest paths in dynamic directed graphs. In these problems, an update can change all edges incident to a node. The basic queries on reachability and distances should be answered in constant time, but also paths should be produced in time proportional to their length. For: Transitive closure of Demetrescu and Italiano (FOCS 2000) Space reduction from O(n3) to O(n2), preserving an amortized update time of O(n2). Exact all-pairs shortest dipaths of King (FOCS 1999) Space reduction from Õ(n3) to Õ(n2√nb), preserving an amortized update time of Õ(n2√nb), where b is the maximal edge weight. Approximate all-pairs shortest dipaths of King (FOCS 1999) Space reduction from Õ(n3) to Õn2, preserving an amortized update time of Õn2. Several authors (Demetrescu and Italiano, FOCS 2000, and Brown and King, Oberwolfach 2000) had discovered techniques to give a corresponding space reduction, but these techniques could be used to show only the existence of a desired dipath, and could not be used to produce the actual path.