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Chvátal defined a skew partition of a graph G to be a partition of its vertex set into two non-empty parts A and B such that A induces a disconnected subgraph of G and B induces a disconnected subgraph of G. Skew partitions are important in the characterization of perfect graphs. De Figuereido et al. presented a polynomial time algorithm which given a graph… (More)

An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete mul-tipartite graph or a… (More)

A fundamental problem in computational biology is the phylogeny reconstruction for a set of specific organisms. One of the graph theoretical approaches is to construct a similarity graph on the set of organisms where adjacency indicates evolutionary closeness, and then to reconstruct a phylogeny by computing a tree interconnecting the organisms such that… (More)

Reconstruction of an evolutionary history for a set of organisms is an important research subject in computational biology. One approach motivated by graph theory constructs a relationship graph based on pairwise evolutionary closeness. The approach builds a tree representation equivalent to this graph such that leaves of the tree, corresponding to the… (More)

Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric characteristic of real-life networks, namely their hyperbolicity. In smooth geometry, hyperbolicity captures the notion of… (More)

A lemma of Fouquet implies that a claw-free graph contains an induced C 5 , contains no odd hole, or is quasi-line. In this paper we use this result to give an improved shortest-odd-hole algorithm for claw-free graphs by exploiting the structural relationship between line graphs and quasi-line graphs suggested by Chudnovsky and Seymour's structure theorem… (More)

Many graph processing algorithms require determination of shortest-path distances between arbitrary numbers of node pairs. Since computation of exact distances between all node-pairs of a large graph, e.g., 10M nodes and up, is prohibitively expensive both in computational time and storage space, distance approximation is often used in place of exact… (More)

Given a set S = {C1, ..., C k } of Boolean circuits, we show how to construct a universal for S circuit C0, which is much smaller than Valiant's universal circuit or a circuit incorporating all C1,. , we embed them in a new graph D0. The embedding is such that a secure computation of any of C1, ..., C k is possible by a corresponding secure computation over… (More)

A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this article, we address these weaknesses by describing mechanisms to choose alternate next hops. Our first contribution is to… (More)

We provide a quasilinear time algorithm for the p-center problem with an additive error less than or equal to 3 times the input graph's hyperbolic constant. Specifically, for the graph G = (V, E) with n vertices, m edges and hyperbolic constant δ, we construct an algorithm for p-centers in time O(p(δ + 1)(n + m) log(n)) with radius not exceeding r p + δ… (More)