Prasad Chebolu

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An n-lift of a digraph K, is a digraph with vertex set V (K)× [n] and for each directed edge (i, j) ∈ E(K) there is a perfect matching between fibers {i} × [n] and {j} × [n], with edges directed from fiber i to fiber j. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that if h is(More)
We give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian generalized series-parallel graph, and show how to adapt this algorithm to exactly sample a random ET of the given generalized series-parallel graph. Note that the class of generalized seriesparallel graphs includes all outerplanar graphs. We can(More)
In recent years there has been considerable interest in analyzing random graph models for the Web. We consider two such models - the Random Surfer model, introduced by Blum et al. [7], and the PageRank-based selection model, proposed by Pandurangan et al. [18]. It has been observed that search engines influence the growth of the Web. The PageRank-based(More)
We investigate the complexity of approximately counting stable matchings in the k-attribute model, where the preference lists are determined by dot products of “preference vectors” with “attribute vectors”, or by Euclidean distances between “preference points“ and “attribute points”. Irving and Leather [16] proved that counting the number of stable(More)
In this paper we give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The problems of counting ETs are known to be ♯P complete for general graphs (Brightwell and Winkler, 2005 [4]). To date, no polynomial-time algorithm for counting Euler tours of any class of graphs is known(More)
We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the k-attribute model, in which the preference lists are determined by dot products of “preference vectors” with “attribute vectors” and (ii) the k-Euclidean model, in which the preference lists are determined by the closeness of the “positions” of the(More)
We explore the average-case “Vickrey” cost of structures in a random setting: the Vickrey cost of a shortest path in a complete graph or digraph with random edge weights; the Vickrey cost of a minimum spanning tree (MST) in a complete graph with random edge weights; and the Vickrey cost of a perfect matching in a complete bipartite graph with random edge(More)
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