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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)
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 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)
We present a new linear-time algorithm to find the immediate dominators of all vertices in a flowgraph. Our algorithm is simpler than previous linear-time algorithms: rather than employ complicated data structures, we combine the use of microtrees and memoization with new observations on a restricted class of path compressions. We have implemented our(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)
We study the parameterized complexity of three NP-hard graph completion problems. The MINIMUM FILL-IN problem is to decide if a graph can be triangulated by adding at most k edges. We d e v elop an O(k 2 mn + f(k)) algorithm for this problem on a graph with n vertices and m edges. In particular, this implies that the problem is xed-parameter tractable(More)
We present approximation schemes for \dense" instances of many well-known NP-hard problems, including 0-1 quadratic-assignment, (an optimization formulation of) graph-isomorphism, 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 2); denseness for the other(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)