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Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems to Internet routing. Some of these applications involve huge graphs and yet require fast query answering. We propose a new data structure for representing all distances in a graph. The data structure is <i>distributed</i> in the(More)
We present algorithms to label the nodes of an XML tree which is subject to insertions and deletions of nodes. The labeling is done such that (1) we label each node immediately when it is inserted and this label remains unchanged, and (2) from a pair of labels alone, we can decide whether one node is an ancestor of the other. This problem arises in the(More)
A directed multigraph is said to be <i>d</i>-regular if the indegree and outdegree of every vertex is exactly <i>d</i>. By Hall's theorem, one can represent such a multigraph as a combination of at most <i>n</i><sup>2</sup> cycle covers, each taken with an appropriate multiplicity. We prove that if the <i>d</i>-regular multigraph does not contain more than(More)
We study the point-to-point shortest path problem in a setting where preprocessing is allowed. We improve the reach-based approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both(More)
The graph sandwich problem for property is de ned as follows: Given two graphs G1 = (V;E1) and G2 = (V;E2) such that E1 E2, is there a graph G = (V;E) such that E1 E E2 which satis es property ? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we(More)
Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete binary trees is straightforward. Furthermore, for complete(More)
We present approximation schemes for \dense" instances of many well-known NP-hard problems, including 0-1 quadratic-assignment, (an optimization formulation of) graphisomorphism, min-cut-linear-arrangement, max-acyclic-subgraph, betweenness, and min-linear-arrangment. (A \dense" graph is one in which the number of edges is (n); denseness for the other(More)
The basic question that Economics deals with is how to “best” allocate scarce resources. The basic answer is that trade can improve everyone’s welfare, and will lead to a market equilibrium: a vector of resource prices that “clear the market” and lead to an efficient allocation. Indeed, Arrow and Debreu and much further work show that such market equilibria(More)
Physical mapping is a central problem in molecular biology and the human genome project. The problem is to reconstruct the relative position of fragments of DNA along the genome from information on their pairwise overlaps. We show that four simplified models of the problem lead to NP-complete decision problems: Colored unit interval graph completion, the(More)