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

This booklet constitutes the refereed lawsuits of the thirteenth Annual ecu 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 rigorously reviewed and chosen from 244 submissions. The papers deal with all present concerns in algorithmics achieving from layout and mathematical concerns over real-world purposes in a number of fields as much as engineering and research of algorithms.

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**Extra info for Algorithms – ESA 2005: 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005. Proceedings**

**Sample text**

4 for an example. Then we relocate to v and continue ﬁnishing the current chain C. (3) If v = w and w holds a token π which is a forefather of τ (if w holds several such tokens, we choose an arbitrary one), we cannot move the subtree rooted at π below τ . Instead, we either create a new cluster or extend the current cluster. Note that it can happen that π = τ . We distinguish a few cases. If π is an ancestor of τ in TK , then we just closed a cycle D containing v and w. The part of D from w to v consists of edges that are initial parts of the token paths of all predecessors of τ up to π, see Fig.

Explored nodes may be explored again by other exploration nodes, but it is forbidden to ﬂood any occupied node again. These two marks are only valid for a speciﬁc round of the BFS, that corresponds to a speciﬁc search depth. This way we only forbid to ﬂood a region twice with the same search depth. Lemma 2. The Traverse and Search algorithm is O(1)-time-competitive. Lemma 3. Given a g × g mesh with total perimeter size p. The Traverse and Search algorithm produces traﬃc O(g + min{g 2 log g, p2 log g}).

Therefore, we consider a mesh network with faulty parts as underlying model, which enables us to study the impact of parallelism on the time needed for reaching the destination. 2 Barriers, Borders and Traversal In this paper we consider a two-dimensional mesh network with faulty nodes. The network is deﬁned by a set of nodes V ⊆ N × N and a set of edges E := {(v, w) : v, w ∈ V ∧ |vx − wx | + |vy − wy | = 1}. A node v is identiﬁed by its position (vx , vy ) ∈ N × N in the mesh. There is no restriction on the size of the network, because we analyze time and traﬃc with respect to the position of the given start and target node in the network.