Abstract
This paper considers compact fault-tolerant routing schemes for weighted general graphs, namely, routing schemes that avoid a set of failed (or forbidden) edges. We present a compact routing scheme capable of handling multiple edge failures. Assume a source node s contains a message M designated to a destination target t and assume a set F of edges crashes (unknown to s). Our scheme routes the message to t (provided that s and t are still connected in G ∖ F) over a path whose length is proportional to the distance between s and t in G ∖ F, to |F|3 and to some poly-log factor. The routing table required at a node v is of size proportional to the degree of v in G and some poly-log factor. This improves on the previously known fault-tolerant compact routing scheme for general graphs, which was capable of overcoming at most 2 edge failures.
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References
Abraham, I., Chechik, S., Gavoille, C., Peleg, D.: Forbidden-set distance labels for graphs of bounded doubling dimension. In: PODC, pp. 192–200 (2010)
Alstrup, S., Brodal, G.S., Rauhe, T.: New Data Structures for Orthogonal Range Searching. In: Proc. 41st IEEE Symp. on Foundations of Computer Science (FOCS), pp. 198–207 (2001)
Awerbuch, B., Bar-Noy, A., Linial, N., Peleg, D.: Improved routing strategies with succinct tables. J. Algorithms, 307–341 (1990)
Awerbuch, B., Kutten, S., Peleg, D.: On buffer-economical store-and-forward deadlock prevention. In: Proc. INFOCOM, pp. 410–414 (1991)
Awerbuch, B., Peleg, D.: Sparse partitions. In: 31st FOCS, pp. 503–513 (1990)
Chechik, S., Langberg, M., Peleg, D., Roditty, L.: f-sensitivity distance oracles and routing schemes. In: 18th ESA, pp. 84–96 (2010)
Cohen, E.: Fast algorithms for constructing t-spanners and paths with stretch t. In: Proc. IEEE Symp. on Foundations of Computer Science, pp. 648–658 (1993)
Courcelle, B., Twigg, A.: Compact forbidden-set routing. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 37–48. Springer, Heidelberg (2007)
Cowen, L.J.: Compact routing with minimum stretch. J. Alg. 38, 170–183 (2001)
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2008)
Duan, R., Pettie, S.: Connectivity oracles for failure prone graphs. In: Proc. ACM STOC (2010)
Eilam, T., Gavoille, C., Peleg, D.: Compact routing schemes with low stretch factor. J. Algorithms 46, 97–114 (2003)
Fraigniaud, P., Gavoille, C.: Memory requirement for universal routing schemes. In: 14th PODC, pp. 223–230 (1995)
Gavoille, C., Gengler, M.: Space-efficiency for routing schemes of stretch factor three. J. Parallel Distrib. Comput. 61, 679–687 (2001)
Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Distributed Computing 16, 111–120 (2003)
Peleg, D.: Distributed computing: a locality-sensitive approach. SIAM, Philadelphia (2000)
Peleg, D., Upfal, E.: A trade-off between space and efficiency for routing tables. J. ACM 36(3), 510–530 (1989)
Thorup, M., Zwick, U.: Compact routing schemes. In: Proc. 13th ACM Symp. on Parallel Algorithms and Architectures (SPAA), pp. 1–10 (2001)
Thorup, M., Zwick, U.: Approximate distance oracles. J. ACM 52, 1–24 (2005)
Twigg, D.A.: Forbidden-set Routing. PhD thesis, University of Cambridge, King’s College (2006)
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Chechik, S. (2011). Fault-Tolerant Compact Routing Schemes for General Graphs. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_7
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DOI: https://doi.org/10.1007/978-3-642-22012-8_7
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