By Jon M. Kleinberg, Ravi Kumar, Prabhakar Raghavan, Sridhar Rajagopalan (auth.), Takano Asano, Hideki Imai, D. T. Lee, Shin-ichi Nakano, Takeshi Tokuyama (eds.)

The abstracts and papers during this quantity have been offered on the 5th Annual overseas Computing and Combinatorics convention (COCOON ’99), which used to be held in Tokyo, Japan from July 26 to twenty-eight, 1999. the themes conceal so much points of theoretical machine technology and combinatorics concerning computing. in keeping with the decision for papers, 88 fine quality prolonged abstracts have been submitted across the world, of which forty six have been chosen for presentation by means of the p- gram committee. each submitted paper was once reviewed by means of at the least 3 software committee participants. lots of those papers symbolize reviews on carrying on with - seek, and it really is anticipated that the majority of them will seem in a extra polished and whole shape in scienti c journals. as well as the normal papers, this v- ume comprises abstracts of 2 invited plenary talks via Prabhakar Raghavan and Seinosuke Toda. The convention additionally integrated a unique speak through Kurt Mehlhorn on LEDA (Library of E cient facts forms and Algorithms). The Hao Wang Award (inaugurated at COCOON ’97) is given to honor the paper judged through this system committee to have the best scienti c advantage. The recipients of the Hao Wang Award 1999 have been Hiroshi Nagamochi and Tos- cover Ibaraki for his or her paper \An Approximation for locating a Smallest 2-Edge- hooked up Subgraph Containing a Speci ed Spanning Tree".

**Read Online or Download Computing and Combinatorics: 5th Annual International Conference, COCOON’99 Tokyo, Japan, July 26–28, 1999 Proceedings PDF**

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**Additional resources for Computing and Combinatorics: 5th Annual International Conference, COCOON’99 Tokyo, Japan, July 26–28, 1999 Proceedings**

**Sample text**

Our purpose of this section is to prove that for all graphs G with sw(G) ≤ k and all subsets S, T of the node set of G, REACHk (G, S, T ) holds if and only if there exists a path on G between S and T . That is, we will prove the following theorem throughout the whole of this section. Note that the statement (a) and (b) below are the core claims of the theorem and the other statements are technically used to prove the core claims. Toda Theorem 1. Let k be any nonnegative integer, let G = (V, E) be any graph, and let S, T be any subset of V .

Definition 1. We define a layout of G to be a bijection from V to the set {1, 2, · · · , |V |}. We also call each element of the set {1, · · · , |V |} a location when dealing with any layout of G. Let ϕ be a layout of G. t. ϕ) if either ϕ(u) ≤ i < ϕ(v) or ϕ(v) ≤ i < ϕ(u). We denote by Eϕ (i) the set of all edges crossing a location i. Furthermore, we say that a path on G crosses a location if the path contains an edge that crosses the location. For a location i, we define Vϕ− (i), Vϕ+ (i), and Vϕ∗ (i) as follows: Vϕ− (i) = {u ∈ VG [Eϕ (i)] : ϕ(u) ≤ i}, Vϕ+ (i) = {v ∈ VG [Eϕ (i)] : i < ϕ(v)}, Vϕ∗ (i) = Vϕ− (i) if |Vϕ− (i)| ≤ |Vϕ+ (i)| Vϕ+ (i) otherwise Then we define the separation-width of G with respect to ϕ, denoted by swϕ (G), by swϕ (G) = max {|Vϕ∗ (i)| : 1 ≤ i ≤ |V |}.

For each unmatched vertex w ∈ W , E must contain an edge ew = (w, z) ∈ E ∩E(w) to cover the leaf edge of w; we fix an edge ew even if |E ∩ E(w)| ≥ 2. , (w, w ) ∈ Eprime ∩ E ). We call such a prime leaf tree T [D(u)] a dangerous tree, and denote by Ld the set of leaf vertices of all dangerous trees (hence |Ld |/2 is the number of all dangerous trees). Thus, we have E − M ⊇ Eprime ∩ E , where |Eprime ∩ E | = |Ld |/2. Also the number of edges ew with w ∈ W − Ld is |{ew | w ∈ W − Ld }| = |W | − |Ld |.