Sanjiv Kapoor

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The problem of finding a rectilinear shortest path amongst obstacles may be stated as follows: Given a set of obstacles in the plane find a shortest rectilinear (<italic>L</italic><subscrpt>1</subscrpt>) path from a point <italic>s</italic> to a point <italic>t</italic> which avoids all obstacles. The path may touch an obstacle but may not cross an(More)
In the first part of the paper, we extend Karmarkar's interior point method to give an algorithm for Convex Quadratic Programming which requires O(Na'~7(logL)(logN)L) arithmetic operations. At each iteration, Karmarkar's method locally minimizes the linear (convex) numerator of a transformed objective function in the transformed domain. However, in the case(More)
In this paper we address the issue of designing multipath routing algorithms. Multi-path routing has the potential of improving the throughput but requires buffers at the destination. Our model assumes a network with capacitated edges and a delay function associated with the network links (edges). We consider the problem of establishing a specified(More)
In this paper, we present algorithms for enumeration of spanning trees in undi-rected graphs, with and without weights. The algorithms use a search tree technique to construct a computation tree. The computation tree can be used to output all spanning trees by outputting only relative changes between spanning trees rather than the entire spanning trees(More)
This paper describes an efficient algorithm for the geodesic shortest, nath oroblem. i.e. the problem of finding shortest path; bet&n pa& of points on the surface of a 3dimensional polyhedron such that the path is constrained to lie on the surface of the polyhedron. We use the wavefront method and show an O(nlog%) time bound for this problem, when there are(More)
In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The <i>market equilibrium problem</i> is to compute a price vector which ensures market clearing, i. e. the demand of a good equals its supply, and given the prices,(More)
Let <?Pub Fmt italic>S<?Pub Fmt /italic> be a set of <?Pub Fmt italic>n<?Pub Fmt /italic> points in <inline-equation> <f> <sc><blkbd>R<sup><it>D</it></sup></blkbd></sc></f> </inline-equation>. It is shown that a range tree can be used to find an <inline-equation> <f> <it>L<inf>&#8734;</inf></it></f> </inline-equation>-nearest neighbor in <italic>S</italic>(More)