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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)
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 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 parameterizedcomplexityof three NP-hard graph completionproblems. The MINIMUM FILL-IN problem is to decide if a graph can be triangulated by adding at most k edges. We develop O(c k m) and O(k 2 mn + f(k)) algorithms for this problem on a graph with n vertices and m edges. Here f(k) is exponential in k and the constants hidden by the big-O(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(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 recent seminal result of Racke is that for any network there is an oblivious routing algorithm with a polylog competitive ratio with respect to congestion. Unfortunately, Racke's construction is not polynomial time. We give a polynomial time construction that guarantee's Racke's bounds, and more generally gives the true optimal ratio for any network.