Results 1 
9 of
9
Searching for a black hole in arbitrary networks
 Distributed Computing
, 2002
"... Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, ..."
Abstract

Cited by 40 (24 self)
 Add to MetaCart
Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topologyindependent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a sizeoptimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance ∆ + 1 agents are needed and suffice, and the cost is Θ(n 2), where ∆ is the maximal degree of a node and n is the number of nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n 2); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upperbound proofs are constructive.
Algorithms and Orders for Finding Noncommutative Gröbner Bases
, 1997
"... The problem of choosing efficient algorithms and good admissible orders for computing Gröbner bases in noncommutative algebras is considered. Gröbner bases are an important tool that make many problems in polynomial algebra computationally tractable. However, the computation of Grobner bases is expe ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
The problem of choosing efficient algorithms and good admissible orders for computing Gröbner bases in noncommutative algebras is considered. Gröbner bases are an important tool that make many problems in polynomial algebra computationally tractable. However, the computation of Grobner bases is expensive, and in noncommutative algebras is not guaranteed to terminate. The algorithm, together with the order used to determine the leading term of each polynomial, are known to affect the cost of the computation, and are the focus of this thesis. A Gröbner basis is a set of polynomials computed, using Buchberger's algorithm, from another set of polynomials. The noncommutative form of Buchberger's algorithm repeatedly constructs a new polynomial from a triple, which is a pair of polynomials whose leading terms overlap and form a nontrivial common multiple. The algorithm leaves a number of details underspecified, and can be altered to improve its behavior. A significant improvement is the devel...
A LinearTime Algorithm for FourPartitioning FourConnected Planar Graphs (Extended Abstract)
 143
, 1997
"... Given a graph G = (V; E), k distinct vertices u 1 ; u 2 ; 1 1 1, u k 2 V and k natural numbers n 1 ; n 2 ; 1 1 1 ; n k such that P k i=1 n i = jV j, we wish to find a partition V 1 ; V 2 ; 1 1 1 ; V k of the vertex set V such that u i 2 V i , jV i j = n i , and V i induces a connected subgraph of G ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Given a graph G = (V; E), k distinct vertices u 1 ; u 2 ; 1 1 1, u k 2 V and k natural numbers n 1 ; n 2 ; 1 1 1 ; n k such that P k i=1 n i = jV j, we wish to find a partition V 1 ; V 2 ; 1 1 1 ; V k of the vertex set V such that u i 2 V i , jV i j = n i , and V i induces a connected subgraph of G for each i, 1 i k. Such a partition is called a k partition of G. The problem of finding a kpartition of a general graph is NPhard [DF85], and hence it is very unlikely that there is a polynomialtime algorithm to solve the problem. Although not every graph has a kpartition, Gyori and Lov'asz independently proved that every kconnected graph has a kpartition for any u 1 ; u 2 ; 1 1 1 ; u k and n 1 ; n 2 ; 1 1 1 ; n k [G78, L77]. However, their proofs do not yield any polynomialtime algorithm for actually finding a k ...
A note on Arbitrarily vertex decomposable graphs, Opuscula Mathematica 26
, 2006
"... A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n1,...,nk) of positive integers such that n1 +... + nk = n there exists a partition (V1,...,Vk) of the vertex set of G such that for each i ∈ {1,...,k}, Vi induces a connected subgraph of G on ni vertices. In th ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n1,...,nk) of positive integers such that n1 +... + nk = n there exists a partition (V1,...,Vk) of the vertex set of G such that for each i ∈ {1,...,k}, Vi induces a connected subgraph of G on ni vertices. In this paper we show that if G is a twoconnected graph on n vertices with the independence number at most ⌈n/2 ⌉ and such that the degree sum of any pair of nonadjacent vertices is at least n − 3, then G is arbitrarily vertex decomposable. We present another result for connected graphs satisfying a similar condition where the bound n − 3 is replaced by n − 2. 1
Efficient Algorithms for Drawing Planar Graphs
, 1999
"... x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ................. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ............................ 6 1.2.4 Orthogonal drawings . . ........................... 7 1.2.5 Grid drawings ................................ 8 1.3 Properties of Drawings ................................ 9 1.4 Scope of this Thesis .................................. 10 1.4.1 Rectangular drawings . . . ......................... 11 1.4.2 Orthogonal drawings . . ........................... 12 1.4.3 Boxrectangular drawings ........................... 14 1.4.4 Convex drawings . . ............................. 16 1.5 Summary ....................................... 16 2 Preliminaries 20 2.1 Basic Terminology .................................. 20 2.1.1 Graphs and Multigraphs ........................... 20 i CO...
Structural properties of recursively partitionable graphs with connectivity 2 ∗
, 2012
"... A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1,..., np) of V (G)  there exists a partition (V1,..., Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namel ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1,..., np) of V (G)  there exists a partition (V1,..., Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OLAP and RAP for short, respectively), in which the subgraphs induced by a partition of G must not only be connected but also fulfil additional conditions. In this paper, we point out some structural properties of OLAP and RAP graphs with connectivity 2. In particular, we show that deleting a cut pair of these graphs results in a graph with a bounded number of components, some of whom have a small number of vertices. We obtain these results by studying a simple class of 2connected graphs called balloons. 1
unknown title
"... Noname manuscript No. (will be inserted by the editor) On the complexity of partitioning a graph into a few connected subgraphs ..."
Abstract
 Add to MetaCart
Noname manuscript No. (will be inserted by the editor) On the complexity of partitioning a graph into a few connected subgraphs