TY - GEN

T1 - Prioritized metric structures and embedding

AU - Elkin, Michael

AU - Filtser, Arnold

AU - Neiman, Ofer

PY - 2015/6/14

Y1 - 2015/6/14

N2 - Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms, online algorithms, distributed algorithms and for computing sparsifiers. However, this methodology appears to have a limitation: the worst-case performance inherently depends on the cardinality of the metric, and one could not specify in advance which vertices/points should enjoy a better service (i.e., stretch/distortion, label size/dimension) than that given by the worst-case guarantee. In this paper we alleviate this limitation by devising a suit of prioritized metric data structures and embeddings. We show that given a priority ranking (x1,x2, . . . ,xn) of the graph vertices (respectively, metric points) one can devise a metric data structure (respectively, embedding) in which the stretch (resp., distortion) incurred by any pair containing a vertex xj will depend on the rank j of the vertex. We also show that other important parameters, such as the label size and (in some sense) the dimension, may depend only on j. In some of our metric data structures (resp., embeddings) we achieve both prioritized stretch (resp., distortion) and label size (resp., dimension) simultaneously. The worst-case performance of our metric data structures and embeddings is typically asymptotically no worse than of their non-prioritized counterparts.

AB - Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms, online algorithms, distributed algorithms and for computing sparsifiers. However, this methodology appears to have a limitation: the worst-case performance inherently depends on the cardinality of the metric, and one could not specify in advance which vertices/points should enjoy a better service (i.e., stretch/distortion, label size/dimension) than that given by the worst-case guarantee. In this paper we alleviate this limitation by devising a suit of prioritized metric data structures and embeddings. We show that given a priority ranking (x1,x2, . . . ,xn) of the graph vertices (respectively, metric points) one can devise a metric data structure (respectively, embedding) in which the stretch (resp., distortion) incurred by any pair containing a vertex xj will depend on the rank j of the vertex. We also show that other important parameters, such as the label size and (in some sense) the dimension, may depend only on j. In some of our metric data structures (resp., embeddings) we achieve both prioritized stretch (resp., distortion) and label size (resp., dimension) simultaneously. The worst-case performance of our metric data structures and embeddings is typically asymptotically no worse than of their non-prioritized counterparts.

KW - Distance oracles

KW - Metric embedding

KW - Priorities

KW - Routing

UR - http://www.scopus.com/inward/record.url?scp=84958763978&partnerID=8YFLogxK

U2 - 10.1145/2746539.2746623

DO - 10.1145/2746539.2746623

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AN - SCOPUS:84958763978

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 489

EP - 498

BT - STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing

PB - Association for Computing Machinery

T2 - 47th Annual ACM Symposium on Theory of Computing, STOC 2015

Y2 - 14 June 2015 through 17 June 2015

ER -