A separator theorem for graphs of bounded genus
Journal of Algorithms
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Labeling schemes for flow and connectivity
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Reachability and distance queries via 2-hop labels
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved labeling scheme for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Short and Simple Labels for Small Distances and Other Functions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Labeling Schemes for Dynamic Tree Networks
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Query efficient implementation of graphs of bounded clique-width
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On-the-fly maintenance of series-parallel relationships in fork-join multithreaded programs
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On distance constrained labeling of disk graphs
Theoretical Computer Science
Roads, codes, and spatiotemporal queries
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Distance labeling schemes for well-separated graph classes
Discrete Applied Mathematics
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed verification of minimum spanning trees
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Informative labeling schemes for graphs
Theoretical Computer Science - Mathematical foundations of computer science 2000
Interval routing in reliability networks
Theoretical Computer Science - Foundations of software science and computation structures
Distance and routing labeling schemes for non-positively curved plane graphs
Journal of Algorithms
Average case analysis for tree labelling schemes
Theoretical Computer Science
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Trade-offs between the size of advice and broadcasting time in trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Localization and routing in sensor networks by local angle information
ACM Transactions on Sensor Networks (TOSN)
Query efficient implementation of graphs of bounded clique-width
Discrete Applied Mathematics
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
Labeling schemes for weighted dynamic trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Communication algorithms with advice
Journal of Computer and System Sciences
An optimal ancestry scheme and small universal posets
Proceedings of the forty-second ACM symposium on Theory of computing
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
DISC'10 Proceedings of the 24th international conference on Distributed computing
Indexing Network Structure with Shortest-Path Trees
ACM Transactions on Knowledge Discovery from Data (TKDD)
A note on labeling schemes for graph connectivity
Information Processing Letters
Average case analysis for tree labelling schemes
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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
The exact distance to destination in undirected world
The VLDB Journal — The International Journal on Very Large Data Bases
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Temporal network optimization subject to connectivity constraints
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases. We obtain upper bounds and (most importantly) lower bounds for several interesting families of graphs. In particular, our main results are the following:For general graphs, the length needed is &THgr;(n).For trees, the length needed is &THgr;(log2 n).For planar graphs, we show an upper bound of &Ogr;(√n log n) and a lower bound of &OHgr;(n1/3).For bounded degree graphs, we show a lower bound of &OHgr;(√n).The upper bounds for planar graphs and for trees follow by a more general upper bound for graphs with a r(n)- separator. The two lower bounds, however, are obtained by two different arguments that may be interesting in their own right.We also show some lower bounds on the length of the labels, even if it is only required that distances be approximated to a multiplicative factor s. For example, we show that for general graphs the required length is &OHgr;(n). We also consider the problem of the time complexity of the distance function once the labels are computed. We show that there are graphs with optimal labels of length 3 log n, such that if we use any labels with fewer than n bits per label, computing the distance function requires exponential time. A similar result is obtained for planar and bounded degree graphs.