By Michael Mitzenmacher (auth.), Amos Fiat, Peter Sanders (eds.)

This booklet constitutes the refereed complaints of the seventeenth Annual eu Symposium on Algorithms, ESA 2009, held in Copenhagen, Denmark, in September 2009 within the context of the mixed convention ALGO 2009.

The sixty seven revised complete papers awarded including three invited lectures have been conscientiously reviewed and chosen: fifty six papers out of 222 submissions for the layout and research tune and 10 out of 36 submissions within the engineering and functions music. The papers are geared up in topical sections on bushes, geometry, mathematical programming, algorithmic video game conception, navigation and routing, graphs and element units, bioinformatics, instant communiations, flows, matrices, compression, scheduling, streaming, on-line algorithms, bluetooth and dial a journey, decomposition and protecting, set of rules engineering, parameterized algorithms, information buildings, and hashing and lowest universal ancestor.

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**Example text**

Definition 3. For T = (V, E), U ⊆ V , and |U | ≥ 2, let Center(T, U ) be one of the nodes v ∈ V such that every tree in T \ {v} (the subgraph of T induced by V \ {v}) contains at most |U |/2 points of U . For U = V , there are either one or two vertices v with this property. In the latter case, the procedure Center(T, U ) in Figure 4 picks an arbitrary one of them. For Eﬃcient Computation of the Characteristic Polynomial of a Tree 17 Procedure Select-Root: Input: A tree T = (V, E) and a subset U ⊆ V .

In the IP, for all i, j such that (Ai , Bj ) is a superedge, choose u ∈ Ai , v ∈ Bj such that u, v are both chosen and set fuv = 1; set fu v = 0 for all other u ∈ Ai , v ∈ Bj . ) 26 M. Charikar, M. Hajiaghayi, and H. Karloﬀ Our algorithm, called MinRepAlg, for rounding LP 1 is relatively simple, though its proof is involved and is based on an interesting generalization of the birthday paradox. The algorithm is as follows. Find an optimal solution f ∗ , p∗ to LP 1. √ For each x ∈ A ∪ B, let p1x = min{1, qpx }.

Output: The vector (a0 , a1 , . . , a n/2 ) where ar is the number of r-matchings in T . (a0 + a1 x + · · · + a n/2 x Return (a0 , . . , a n/2 ) n/2 ) = Restricted-Matchings(T, ∅) Fig. 2. The algorithm Matchings and the characteristic polynomial χ(G; λ), namely χ(G; λ) = λn fM (G; −λ−2 ) This is a direct consequence of the characterization of the coeﬃcients cr of the characteristic polynomial for forests. , [1, p. 49]). Thus, we could actually have used the characteristic polynomial directly in our algorithms.