TY - GEN

T1 - An optimal ancestry scheme and small universal posets

AU - Fraigniaud, Pierre

AU - Korman, Amos

PY - 2010

Y1 - 2010

N2 - In this paper, we solve the ancestry problem, which was introduced more than twenty years ago by Kannan et al. [STOC '88], and is among the most well-studied problems in the field of informative labeling schemes. Specifically, we construct an ancestry labeling scheme for n-node trees with label size log2 n + O(log log n) bits, thus matching the log 2 n + Ω(log log n) bits lower bound given by Alstrup et al. [SODA '03]. Besides its optimal label size, our scheme assigns the labels in linear time, and guarantees that any ancestry query can be answered in constant time. In addition to its potential impact in terms of improving the performances of XML search engines, our ancestry scheme is also useful in the context of partially ordered sets. Specifically, for any fixed integer k, our scheme enables the construction of a universal poset of size O(nk log 4k n) for the family of n-element posets with tree-dimension at most k. This bound is almost tight thanks to a lower bound of nk-o(1) due to Alon and Scheinerman [Order '88].

AB - In this paper, we solve the ancestry problem, which was introduced more than twenty years ago by Kannan et al. [STOC '88], and is among the most well-studied problems in the field of informative labeling schemes. Specifically, we construct an ancestry labeling scheme for n-node trees with label size log2 n + O(log log n) bits, thus matching the log 2 n + Ω(log log n) bits lower bound given by Alstrup et al. [SODA '03]. Besides its optimal label size, our scheme assigns the labels in linear time, and guarantees that any ancestry query can be answered in constant time. In addition to its potential impact in terms of improving the performances of XML search engines, our ancestry scheme is also useful in the context of partially ordered sets. Specifically, for any fixed integer k, our scheme enables the construction of a universal poset of size O(nk log 4k n) for the family of n-element posets with tree-dimension at most k. This bound is almost tight thanks to a lower bound of nk-o(1) due to Alon and Scheinerman [Order '88].

KW - informative labeling schemes

KW - partially ordered sets

KW - XML

UR - http://www.scopus.com/inward/record.url?scp=77954712913&partnerID=8YFLogxK

U2 - 10.1145/1806689.1806773

DO - 10.1145/1806689.1806773

M3 - Conference contribution

AN - SCOPUS:77954712913

SN - 9781605588179

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

SP - 611

EP - 619

BT - STOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing

T2 - 42nd ACM Symposium on Theory of Computing, STOC 2010

Y2 - 5 June 2010 through 8 June 2010

ER -