Labeling schemes for flow and connectivity

Authors:
Michal Katz;Nir A. Katz;Amos Korman;David Peleg
Affiliations:
Bar Ilan University, Ramat Gan, 52900, Israel;Bar Ilan University, Ramat Gan, 52900, Israel;The Weizmann Institute of Science, Rehovot, 76100 Israel;The Weizmann Institute of Science, Rehovot, 76100 Israel
Venue:
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2002

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Abstract

This paper studies labeling schemes for flow and connectivity functions. A flow labeling scheme using O(log n ⋅ log ŵ)-bit labels is presented for general n-vertex graphs with maximum (integral) capacity ŵ. This is shown to be asymptotically optimal. For edge-connectivity, this yields a tight bound of Θ(log2 n) bits. A k-vertex connectivity labeling scheme is then given for general n-vertex graphs using at most 3 log n bits for k = 2, 5 log n bits for k = 3 and 2k log n bits for k 3. Finally, a lower bound of Ω(k log n) is established for k-vertex connectivity on n-vertex graphs where k is polylogarithmic in n.