TY - JOUR

T1 - Proximity-preserving labeling schemes

AU - Peleg, David

PY - 2000/3

Y1 - 2000/3

N2 - This article considers informative labeling schemes for graphs. Specifically, the question introduced is whether it is possible to label the vertices of a graph with short labels in such a way that the distance between any two vertices can be inferred from inspecting their labels. A labeling scheme enjoying this property is termed a proximity-preserving labeling scheme. It is shown that for the class of n-vertex weighted trees with M-bit edge weights, there exists such a proximity-preserving labeling scheme using O(M log n + log2 n) bit labels. For the family of all n-vertex unweighted graphs, a labeling scheme is proposed that using O(log2 n · K · n1/k) bit labels can provide approximate estimates to the distance, which are accurate up to a factor of √8k. In particular, using O(log3 n) bit labels the scheme can provide estimates accurate up to a factor of √2 log n. (For weighted graphs, one of the log n factors in the label size is replaced by a factor logarithmic in the network's diameter.)

AB - This article considers informative labeling schemes for graphs. Specifically, the question introduced is whether it is possible to label the vertices of a graph with short labels in such a way that the distance between any two vertices can be inferred from inspecting their labels. A labeling scheme enjoying this property is termed a proximity-preserving labeling scheme. It is shown that for the class of n-vertex weighted trees with M-bit edge weights, there exists such a proximity-preserving labeling scheme using O(M log n + log2 n) bit labels. For the family of all n-vertex unweighted graphs, a labeling scheme is proposed that using O(log2 n · K · n1/k) bit labels can provide approximate estimates to the distance, which are accurate up to a factor of √8k. In particular, using O(log3 n) bit labels the scheme can provide estimates accurate up to a factor of √2 log n. (For weighted graphs, one of the log n factors in the label size is replaced by a factor logarithmic in the network's diameter.)

KW - Approximate-distance

KW - Graph representations

KW - Labeling schemes

UR - http://www.scopus.com/inward/record.url?scp=0034423261&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0118(200003)33:3<167::AID-JGT7>3.0.CO;2-5

DO - 10.1002/(SICI)1097-0118(200003)33:3<167::AID-JGT7>3.0.CO;2-5

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AN - SCOPUS:0034423261

SN - 0364-9024

VL - 33

SP - 167

EP - 176

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 3

ER -