Venkatesh Raman

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We consider the <i>indexable dictionary</i> problem which consists in storing a set <i>S</i> &#8838; {0,&#8230;, <i>m</i> - 1} for some integer <i>m,</i> while supporting the operations of <i>rank</i>(<i>x</i>), which returns the number of elements in <i>S</i> that are less than <i>x</i> if <i>x</i> &#949; <i>S,</i> and -1 otherwise; and(More)
This paper focuses on space efficient representations of rooted trees that permit basic navigation in constant time. While most of the previous work has focused on binary trees, we turn our attention to trees of higher degree. We consider both cardinal trees (or k-ary tries), where each node has k slots, labelled {1,...,k}, each of which may have a(More)
In this paper we investigate the parametrized complexity of the problems MaxSat and MaxCut using the framework developed by Downey and Fellowss7]. Let G be an arbitrary graph having n vertices and m edges, and let f be an arbitrary CNF formula with m clauses on n variables. We improve Cai and Chen's O(2 2k m) time algorithm for determining if at least k(More)
We consider the <i>indexable dictionary</i> problem, which consists of storing a set <i>S</i> &#8838; &lcub;0,&#8230;,<i>m</i> &minus; 1&rcub; for some integer <i>m</i> while supporting the operations of rank(<i>x</i>), which returns the number of elements in <i>S</i> that are less than <i>x</i> if <i>x</i> &#8712; <i>S</i>, and &minus;1 otherwise; and(More)
We consider <i>suc cinct</i> or space-efficient representations of trees that efficiently support a variety of navigation operations. We focus on static <i>ordinal</i> trees, i.e., arbitrary static rooted trees where the children of each node are ordered. The set of operations is essentially the union of the sets of operations supported by previous succinct(More)
The VERTEX COVER problem asks, for input consisting of a graph G on n vertices, and a positive integer k, whether there is a set of k vertices such that every edge of G is incident with at least one of these vertices. We give an algorithm for this problem that runs in time O(kn + (1.324718)'k'). In particular, this gives an 0((1.324718) " n2) algorithm to(More)
We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree and balanced parenthesis expression. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been(More)
We consider new parameterizations of NP-optimization problems that have nontrivial lower and/or upper bounds on their optimum solution size. The natural parameter, we argue, is the quantity above the lower bound or below the upper bound. We show that for every problem in MAX SNP, the optimum value is bounded below by an unbounded function of the input-size,(More)