By Irene Finocchi, Fabrizio Grandoni, Giuseppe F. Italiano (auth.), Gerth Stølting Brodal, Stefano Leonardi (eds.)

This e-book constitutes the refereed court cases of the thirteenth Annual eu Symposium on Algorithms, ESA 2005, held in Palma de Mallorca, Spain, in September 2005 within the context of the mixed convention ALGO 2005.

The seventy five revised complete papers provided including abstracts of three invited lectures have been conscientiously reviewed and chosen from 244 submissions. The papers tackle all present concerns in algorithmics achieving from layout and mathematical matters over real-world functions in a number of fields as much as engineering and research of algorithms.

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A. Bender and D. K. Slonim. The power of team exploration: Two robots can learn unlabeled directed graphs. In Proceedings of the 35th Symposium on Foundations of Computer Science (FOCS’94), pages 75–85, 1994. 5. P. Berman, A. Blum, A. Fiat, H. Karloﬀ, A. Ros´en, and M. Saks. Randomized robot navigation algorithms. In Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms (SODA’96), pages 75–84, 1996. 6. A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain.

Under these ratios we can formalize the intuition telling that ﬂooding as a multipath strategy performs well in mazes and badly in open space, while some single-path strategy performs well in open space, but bad in mazes. The following table shows the competitive time ratio Rt and the comparative traﬃc ratio RTr of a single-path and a multi-path strategy. We consider the barrier Online Routing in Faulty Meshes 29 traversal algorithm described in Section 1 as traﬃc-optimal single-path strategy, and expanding ring search as time-optimal multi-path strategy.

Given a g1 × g1 mesh with total perimeter size p. For all g0 with 1 ≤ g0 ≤ g1 there is a O(1)-time-competitive algorithm for the online frame 2 multicast problem with traﬃc O( gg10 + p · g0 log g0 ). A proof is given in [16]. 2 except for the BFS: The multicast process is started with the level-1 square and begins with the frame traversal. If a barrier prevents a frame node from proceeding with the frame traversal, the frame node becomes exploration node and starts the modiﬁed BFS, which we call level-1 BFS.