Sanjiv Kapoor

Network Lifetime and Power Assignment in ad hoc wireless networks

Used for topology control in ad-hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G=(V,c). The power of a vertex u in a directed spanning subgraph H is given by PH (u) = max uv ∈ E(H) c(uv). The power of H is given by \(p(H) = \sum_{u \in v}p{\sc H}(u)\), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We present asymptotically optimal O(log n)-approximation algorithms for three Power Assignment problems: Min-Power Strong Connectivity, Min-Power Symmetric Connectivity (the undirected graph having an edge uv iff H has both uv and vu must be connected) and Min-Power Broadcast (the input also has r ∈ V , and H must be a r-rooted outgoing spanning arborescence).

Rectilinear shortest paths through polygonal obstacles in O ( n (log n ) 2 ) time

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 obstacle. We study the rectilinear shortest path problem for the case where the obstacles are non-intersecting simple polygons, and present an <italic>&Ogr;</italic>(<italic>n</italic> (log<italic>n</italic>)<supscrpt>2</supscrpt>) algorithm for finding such a path, where <italic>n</italic> is the number of vertices of the obstacles. We also study the case of rectilinear obstacles in three dimensions, and show that <italic>L</italic><subscrpt>1</subscrpt> shortest paths can be found in <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>2</supscrpt>(log <italic>n</italic>)<supscrpt>3</supscrpt>) time.

Efficient computation of geodesic shortest paths

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 O(n) vertices and edges on the polyhedron.

An Efficient Algorithm for Euclidean Shortest Paths Among Polygonal Obstacles in the Plane

Abstract. We give an algorithm to compute a (Euclidean) shortest path in a polygon with h holes and a total of n vertices. The algorithm uses O(n) space and requires

Algorithms for Enumerating All Spanning Trees ofUndirected and Weighted Graphs

O(n+h^2\log n)

Auction algorithms for market equilibrium

time.

Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles

In this paper, we present algorithms for enumeration of spanning trees in undirected 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 themselves. Both the construction of the computation tree and the listing of the trees is shown to require

Optimum lopsided binary trees

O(N+V+E)

Stream-Packing: Resource Allocation in Web Server Farms with a QoS Guarantee

operations for the case of undirected graphs without weights. The basic algorithm is based on swapping edges in a fundamental cycle. For the case of weighted graphs (undirected), we show that the nodes of the computation tree of spanning trees can be sorted in increasing order of weight, in

An Auction-Based Market Equilibrium Algorithm for the Separable Gross Substitutability Case

O(N\log V+VE)