Sanjiv Kapoor

Bio: Sanjiv Kapoor is an academic researcher from Illinois Institute of Technology. The author has contributed to research in topics: Euclidean shortest path & Yen's algorithm. The author has an hindex of 24, co-authored 96 publications receiving 2034 citations. Previous affiliations of Sanjiv Kapoor include Indian Institute of Technology Delhi & Max Planck Society.

Network Lifetime and Power Assignment in ad hoc Wireless Networks

Abstract: 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(logn)2) time

Abstract: 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 (L1) path from a point s to a point t 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 O(n (logn)2) algorithm for finding such a path, where n is the number of vertices of the obstacles. We also study the case of rectilinear obstacles in three dimensions, and show that L1 shortest paths can be found in O(n2(log n)3) time.

Algorithms for Enumerating All Spanning Trees ofUndirected and Weighted Graphs

Abstract: 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 $O(N+V+E)$ 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 $O(N\log V+VE)$ time. The spanning trees themselves can be listed in $O(NV)$ time. Here $N$, $V$, and $E$ refer respectively to the number of spanning trees, vertices, and edges of the graph.

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 $O(n+h^2\log n)$ time.

Efficient computation of geodesic shortest paths

Abstract: 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.

Designing an Super-Peer Network

Abstract: A super-peer is a node in a peer-to-peer network that operates both as a server to a set of clients, and as an equal in a network of super-peers. Super-peer networks strike a balance between the efficiency of centralized search, and the autonomy, load balancing and robustness to attacks provided by distributed search. Furthermore, they take advantage of the heterogeneity of capabilities (e.g., bandwidth, processing power) across peers, which recent studies have shown to be enormous. Hence, new and old P2P systems like KaZaA and Gnutella are adopting super-peers in their design. Despite their growing popularity, the behavior of super-peer networks is not well understood. For example, what are the potential drawbacks of super-peer networks? How can super-peers be made more reliable? How many clients should a super-peer take on to maximize efficiency? we examine super-peer networks in detail, gaming an understanding of their fundamental characteristics and performance tradeoffs. We also present practical guidelines and a general procedure for the design of an efficient super-peer network.

Dynamic Placement of Virtual Machines for Managing SLA Violations

Abstract: A dynamic server migration and consolidation algorithm is introduced. The algorithm is shown to provide substantial improvement over static server consolidation in reducing the amount of required capacity and the rate of service level agreement violations. Benefits accrue for workloads that are variable and can be forecast over intervals shorter than the time scale of demand variability. The management algorithm reduces the amount of physical capacity required to support a specified rate of SLA violations for a given workload by as much as 50% as compared to static consolidation approach. Another result is that the rate of SLA violations at fixed capacity may be reduced by up to 20%. The results are based on hundreds of production workload traces across a variety of operating systems, applications, and industries.

Gross motion planning—a survey

Abstract: Motion planning is one of the most important areas of robotics research. The complexity of the motion-planning problem has hindered the development of practical algorithms. This paper surveys the work on gross-motion planning, including motion planners for point robots, rigid robots, and manipulators in stationary, time-varying, constrained, and movable-object environments. The general issues in motion planning are explained. Recent approaches and their performances are briefly described, and possible future research directions are discussed.