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COCOON
2001
Springer

A Space Saving Trick for Directed Dynamic Transitive Closure and Shortest Path Algorithms

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A Space Saving Trick for Directed Dynamic Transitive Closure and Shortest Path Algorithms
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 ˜O(n3 ) to ˜O(n2 √ nb), preserving an amortized update time of ˜O(n2 √ nb), where b is the maximal edge weight. Approximate all-pairs shortest dipaths of King (FOCS 1999) Space reduction from ˜O(n3 ) to ˜O(n2 ), preserving an amortized update time of ˜O(n2 ). Several authors (Demetrescu and Italiano, FOCS 2000, and Brown and King, Oberwolfach 2000) had discovered techniques to give a cor...
Valerie King, Mikkel Thorup
Added 28 Jul 2010
Updated 28 Jul 2010
Type Conference
Year 2001
Where COCOON
Authors Valerie King, Mikkel Thorup
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