Testing the Supermodular-Cut Condition

For a function on a finite set V with f (∅)= f ( V )=0, a digraph D =( V , A ) is called f -connected if it satisfies the f -cut condition, that is, δ D ( X )≥ f ( X ) for any X ⊆ V , where δ D ( X ) is the number of arcs from X to V ∖ X . We show that, for any crossing supermodular function f , the...

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Veröffentlicht in:Algorithmica Jg. 71; H. 4; S. 1065 - 1075
Hauptverfasser: Tanigawa, Shin-Ichi, Yoshida, Yuichi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.04.2015
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
Property testing
Supermodularity
Bounded-degree model
ISSN:0178-4617, 1432-0541
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Zusammenfassung:For a function on a finite set V with f (∅)= f ( V )=0, a digraph D =( V , A ) is called f -connected if it satisfies the f -cut condition, that is, δ D ( X )≥ f ( X ) for any X ⊆ V , where δ D ( X ) is the number of arcs from X to V ∖ X . We show that, for any crossing supermodular function f , the f -connectivity can be tested with a constant number of queries in the general digraph model with average degree bound. As immediate corollaries, we obtain constant-time testers for k -edge-connectivity, rooted-( k , l )-edge-connectivity, and the property of having k arc-disjoint arborescences. We also give a corresponding result for the undirected case.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-013-9842-8