ABSTRACT
Distance labelings -- introduced as a new way to encode graph topology in a distributed fashion -- have been an active area of research (see [1, 2] for details). In both exact and approximate settings, results in distance labelings and compact routing (for an introduction, esp. for definitions of routing tables and headers, see [3]) seem to go hand in hand, but so far these results have been produced separately. It was already known that graphs with constantsized separators such as trees, outerplanar graphs, seriesparallel graphs and graphs of bounded treewidth, support both exact distance labelings and optimal (additive stretch 0, multiplicative stretch 1) compact routing schemes, but there are classes of graphs known to admit exact distance labelings which do not have constant-sized separators. Our main result is to demonstrate that every n-vertex graph which supports an exact distance labeling with O(l(n))-sized labels also supports a compact routing scheme with O(l(n) + log2 n)-sized headers, O(√n(l(n) + log2 n))-sized routing tables, and an additive stretch of 6. Our general result produces the first known compact routing schemes for classes of graphs where no previous compact routing scheme was known, such as permutation graphs.We note that it is possible to improve substantially on our general result for the classes of interval graphs and circular arc graphs (neither of which admits constant-sized separators). In both cases, a compact routing scheme exists with polylogarithmic headers and routing tables, and an additive stretch of 1; due to space constraints, we defer further discussion of these cases to future presentations of this work.
- C. Gavoille, D. Peleg, S. Pérennes, and R. Raz. Distance labeling in graphs. J. Algorithms, 53(1):85--112, 2004. Google ScholarDigital Library
- D. Peleg. Proximity-preserving labeling schemes. Technical Report CS97-23, Department of Mathematics & Computer Science, Weizmann Institute of Science, 1997. Google ScholarDigital Library
- M. Thorup and U. Zwick. Compact routing schemes. In Proc. SPAA 2001: 1--10. Google ScholarDigital Library
Index Terms
- Compact routing with additive stretch using distance labelings
Recommendations
Exact distance labelings yield additive-stretch compact routing schemes
DISC'06: Proceedings of the 20th international conference on Distributed ComputingDistance labelings and compact routing schemes have both been active areas of recent research. It was already known that graphs with constant-sized recursive separators, such as trees, outerplanar graphs, series-parallel graphs and graphs of bounded ...
Sparse spanners vs. compact routing
SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architecturesRouting with multiplicative stretch 3 (which means that the path used by the routing scheme can be up to three times longer than a shortest path) can be done with routing tables of Θ(√n) bits per node. The space lower bound is due to the existence of ...
Compact routing with slack in low doubling dimension
PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computingWe consider the problem of compact routing with slack in networks of low doubling dimension. Namely, we seek name-independent routing schemes with (1+ε) stretch and polylogarithmic storage at each node: since existing lower bound precludes such a scheme,...
Comments