Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
WWW '99 Proceedings of the eighth international conference on World Wide Web
Data on the Web: from relations to semistructured data and XML
Data on the Web: from relations to semistructured data and XML
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Compact labeling schemes for ancestor queries
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Improved Compact Routing Scheme for Chordal Graphs
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
Labeling Schemes for Dynamic Tree Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An Additive Stretched Routing Scheme for Chordal Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Computing
Short labels by traversal and jumping
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
HID: an efficient path index for complex XML collections with arbitrary links
DNIS'05 Proceedings of the 4th international conference on Databases in Networked Information Systems
A dynamic implicit adjacency labelling scheme for line graphs
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
General compact labeling schemes for dynamic trees
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We present a labeling scheme for rooted trees which allows to compute, from the label of v alone, unique identifiers for the ancestors of v that are at distance at most d from v. For any constant d our labeling scheme produce labels of length log n+O(√log n), and for d ∈ O(√log n) the labels are still of length O(log n). In particular, given the labels of two nodes u and v we can determine from the labels alone whether u is the parent of v or vice versa, whether u and v are siblings, and whether u and v are at distance at most d from each other. The need for such labeling scheme arises in several application areas, including in particular communication networks and search engines for large collections ofWeb XML files. In the latter application XML files are viewed as trees, and typical queries ask for XML files containing a particular set of nodes with specific ancestor, parent, or sibling relationships among them.