2039106
Distributed Clustering Algorithm for Finding Virtual Backbone in Ad Hoc Networks
An important objective in designing a protocol is to save scarce resources like energy and bandwidth, and avoid the broadcast storm problem [1]. One way of addressing these problems is by forming a small virtual backbone. In this paper, we present a distributed clustering algorithm for forming a small backbone in ad-hoc network, based on connected dominating set. The time and message complexity of the algorithm is in O(n).
32211361
On Computing a Largest Empty Arbitrarily Oriented Rectangle
Given a set P of n points within a rectangle R, we present an O(n3) time algorithm for computing an arbitrarily oriented empty rectangle of largest area in R that is bounded by a point of P on each of its four sides. We assume that R is large enough to contain such a rectangle.
33854423
Cycles in self-complementary graphs
Abstract Let G be a self-complementary graph of order p ≥ 8. It is shown that for every integer l , 3 ≤ l ≤ p − 2, G has an l -cycle. Further, if G is hamiltonian, then G is pancyclic.
7001903
Distributed object location in a dynamic network
Modern networking applications replicate data and services widely, leading to a need for location-independent routing -- the ability to route queries directly to objects using names independent of the objects' physical locations. Two important properties of a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be efficiently achieved for certain network topologies. To do this, we present a new distributed algorithm that can solve the nearest-neighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton, Rajaraman, and Richa [14].
36356018
Solution of the Hamiltonian problem for self-complementary graphs
Abstract A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such that (i) G − S has more than | S | components, (ii) S induces the complete graph, and (iii) for every u ∈ S and v ∉ S , we have d G ( u ) > d G ( v ), where d G ( u ) denotes the degree of u in G . In this paper it is shown that a non-hamiltonian self-complementary graph G of order p is highly constricted, unless p = 4 N and G is a particular graph G ∗ (4N) . It is also proved that if G is a self-complementary graph of order p (≥8) and π its degree sequence, then G is pancyclic if π has a realization with a hamiltonian cycle, and G has a 2-factor if π has a realization with a 2-factor, unless p = 4 N and G = G ∗ (4N) .
8131766
Segmentation of a piece-wise planar scene from perspective images
We study and compare two novel embedding methods for segmenting feature points of piece-wise planar structures from two (uncalibrated) perspective images. We show that a set of different homographies can be embedded in different ways to a higher-dimensional real or complex space, so that each homography corresponds to either a complex bilinear form or a real quadratic form. Each embedding reveals different algebraic properties and relations of homographies. We give a closed-form segmentation solution for each case by utilizing these properties based on subspace-segmentation methods. These theoretical results show that one can intrinsically segment a piece-wise planar scene from 2-D images without explicitly performing any 3-D reconstruction. The resulting segmentation may make subsequent 3-D reconstruction much better-conditioned. We demonstrate the proposed methods with some convincing experimental results.
5596998
Computing Refined Buneman Trees in Cubic Time
Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n 5) and a space consumption of O(n 4). In this paper, we present an algorithm with running time O(n 3) and space consumption O(n 2). The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.