Results 1  10
of
20
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
Finding Four Independent Trees
"... Motivated by a multitree approach to the design of reliable communication protocols, Itai and Rodeh gave a linear time algorithm for finding two independent spanning trees in a 2connected graph. Cheriyan and Maheshwari gave an O(V  2) algorithm for finding three independent spanning trees in a 3 ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
Motivated by a multitree approach to the design of reliable communication protocols, Itai and Rodeh gave a linear time algorithm for finding two independent spanning trees in a 2connected graph. Cheriyan and Maheshwari gave an O(V  2) algorithm for finding three independent spanning trees in a 3connected graph. In this paper we present an O(V  3) algorithm for finding four independent spanning trees in a 4connected graph. We make use of chain decompositions of 4connected graphs. ∗ Partially supported by NSF VIGRE grant † Supported by CNPq (Proc: 200611/003) – Brazil ‡ Partially supported by NSF grant DMS0245530 and NSA grant MDA9040310052
Independent Spanning Trees With Small Depths in Iterated Line Digraphs
, 1997
"... . We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
. We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths. Keywords. independent spanning trees, line digraphs, vertexconnectivity, de Bruijn digraphs, Kautz digraphs, interconnection networks, broadcasting. 1 Introduction Unless stated otherwise each digraph of this paper is nite and may have loops but not multiarcs. Let G be a digraph. Then V (G) and A(G) denote the vertex set and the arc set of G, respectively. Let (u; v) 2 A(G). Then we say that u is adjacent to v, and v is adjacent from u. Also, it is said that (u; v) is incident to v and incident from u. Let (v; w) 2 A(G). Then we say that (u; v) is adjacent to (v; w), and (v; w) is adjacent from (u; v). Let ...
Resilient multipath routing with independent directed acyclic graphs
 in Proc. IEEE TRANSACTION ON NETWORKING
, 2012
"... Abstract—In this paper, we introduce the concept of Independent Directed Acyclic Graphs (IDAGs) to achieve resilient multipath routing. Linkindependent (Nodeindependent) DAGs satisfy the property that any path from a source to the root on one DAG is linkdisjoint (nodedisjoint) with any path from ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we introduce the concept of Independent Directed Acyclic Graphs (IDAGs) to achieve resilient multipath routing. Linkindependent (Nodeindependent) DAGs satisfy the property that any path from a source to the root on one DAG is linkdisjoint (nodedisjoint) with any path from the source to the root on the other DAG. Given a network, we develop polynomial time algorithms to compute linkindependent and nodeindependent DAGs. The algorithm developed in this paper: (1) achieves multipath routing; (2) guarantees recovery from single link failure; (3) utilizes all possible edges; and (4) achieves all these with at most one bit per packet as overhead when routing is based on destination address and incoming link. We demonstrate the effectiveness of the proposed IDAGs approach by comparing key performance indices to that of the independent trees technique. I.
Dominator tree certification and independent spanning trees. Electronic preprint
"... ar ..."
(Show Context)
Independent Tree Spanners  FaultTolerant Spanning Trees with Distance Guarantees
 IN PROCEEDINGS 24RD INTERNATIONAL WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE, WG'98
, 1998
"... For any fixed rational parameter t 1, a (tree) tspanner of a graph G is a spanning subgraph (tree) T in G such that the distance between every pair of vertices in T is at most t times their distance in G. General tspanners and their variants have multiple applications in the field of communica ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
For any fixed rational parameter t 1, a (tree) tspanner of a graph G is a spanning subgraph (tree) T in G such that the distance between every pair of vertices in T is at most t times their distance in G. General tspanners and their variants have multiple applications in the field of communication networks, distributed systems, and network design. In this paper, we combine the two concepts of simple structured, sparse tspanners and faulttolerance by examining independent tree tspanners. Given a root vertex r, this is a pair of tree tspanners, such that the two paths from any vertex to r are edge disjoint or internally vertex dijoint, respectively. It is shown that a pair of independent tree tspanners can be found in linear time for t ! 3, whereas the problem for arbitrary t 4 is NPcomplete. As a less restrictive concept, we also treat tree trootspanners, where the distance constraint is relaxed. Here, we show that the problem of finding an independent pair of su...
NonSeparating Cycles in 4Connected Graphs
, 2001
"... We prove that given any fixed edge ra in a 4connected graph G, there exists a cycle C through ra such that G − (V (C) − {r}) is 2connected. This will provide the first step in a decomposition for 4connected graphs. We also prove that for any given edge e in a 5connected graph G there exists an ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We prove that given any fixed edge ra in a 4connected graph G, there exists a cycle C through ra such that G − (V (C) − {r}) is 2connected. This will provide the first step in a decomposition for 4connected graphs. We also prove that for any given edge e in a 5connected graph G there exists an induced cycle C through e in G such that G − V (C) is 2connected. This provides evidence for a conjecture of Lovász.
Chain decompositions of 4connected graphs
, 2003
"... In this paper we give a decomposition of a 4connected graph G into nonseparating chains, which is similar to an ear decomposition of a 2connected graph. We also give an O(V(G)² E(G)) algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improv ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In this paper we give a decomposition of a 4connected graph G into nonseparating chains, which is similar to an ear decomposition of a 2connected graph. We also give an O(V(G)² E(G)) algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to O(V(G)³). This decomposition will be used to find four independent spanning trees in a 4connected graph.
Packing Arborescences
 RIMS KOKYUROKU BESSATSU(2010), B23: 131
, 2010
"... In [7], Edmonds proved a fundamental theorem on packing arborescences that has become the base of several subsequent extensions. Recently, Japanese researchers found an unexpected further generalization which gave rise to many interesting questions about this subject [29], [20]. Another line of rese ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In [7], Edmonds proved a fundamental theorem on packing arborescences that has become the base of several subsequent extensions. Recently, Japanese researchers found an unexpected further generalization which gave rise to many interesting questions about this subject [29], [20]. Another line of researches focused on covering intersecting families which generalizes Edmonds ' theorems in a dierent way. The two approaches was united in [1] by introducing the notion of mixed intersecting biset families. The purpose of this paper is to overview recent developments and to present some new results. We give a polyhedral description of arborescence packable subgraphs based on a connection with biset families, and by using this description we prove TDIness of the corresponding system of inequalities. We also consider the problem of independent trees and arborescences, and give a simple algorithm that decomposes a maximal planar graph into three independent trees.
Nonseparating planar chains in 4connected graphs
, 2002
"... In this paper, we describe an O(V (G)  2) algorithm for finding a “nonseparating planar chain” in a 4connected graph G, which will be used to decompose an arbitrary 4connected graph into “planar chains”. This work was motivated by the study of a multitree approach to reliability in distributed ..."
Abstract
 Add to MetaCart
In this paper, we describe an O(V (G)  2) algorithm for finding a “nonseparating planar chain” in a 4connected graph G, which will be used to decompose an arbitrary 4connected graph into “planar chains”. This work was motivated by the study of a multitree approach to reliability in distributed networks, as well as the study of nonseparating induced paths in highly connected graphs.