Results 11  20
of
51
SublinearTime Approximation of Euclidean Minimum Spanning Tree
, 2003
"... We consider the problem of estimating the weight of a Euclidean minimum spanning tree for a set of n points in R . We focus on the situation when the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a s ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
We consider the problem of estimating the weight of a Euclidean minimum spanning tree for a set of n points in R . We focus on the situation when the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. Our main result is that if we assume the access to the input is supported by a minimal bounding cube of the input, by orthogonal range queries, and by cone approximate nearest neighbors queries, then it is possible to estimate the weight of a Euclidean minimum spanning tree of P to within 1 + " using only e O( n poly(1=")) queries for constant d.
Introduction to testing graph properties
 In Property Testing
, 2010
"... Abstract. The aim of this article is to introduce the reader to the study of testing graph properties, while focusing on the main models and issues involved. No attempt is made to provide a comprehensive survey of this ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
(Show Context)
Abstract. The aim of this article is to introduce the reader to the study of testing graph properties, while focusing on the main models and issues involved. No attempt is made to provide a comprehensive survey of this
Distance approximation in boundeddegree and general sparse graphs
 In Proceedings of the Tenth International Workshop on Randomization and Computation (RANDOM
, 2006
"... We address the problem of approximating the distance of bounded degree and general sparse graphs from having some predetermined graph property P. Namely, we are interested in sublinear algorithms for estimating the fraction of edges that should be added to / removed from a graph so that it obtains P ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
(Show Context)
We address the problem of approximating the distance of bounded degree and general sparse graphs from having some predetermined graph property P. Namely, we are interested in sublinear algorithms for estimating the fraction of edges that should be added to / removed from a graph so that it obtains P. This fraction is taken with respect to a given upper bound m on the number of edges. In particular, for graphs with degree bound d over n vertices, m = dn. To perform such an approximation the algorithm may ask for the degree of any vertex of its choice, and may ask for the neighbors of any vertex. The problem of estimating the distance to having a property was first explicitly addressed by Parnas et. al. (ECCC 2004). In the context of graphs this problem was studied by Fischer and Newman (FOCS 2005) in the densegraphs model. In this model the fraction of edge modifications is taken with respect to n 2, and the algorithm may ask for the existence of an edge between any pair of vertices of its choice. Fischer and Newman showed that every graph property that has a testing algorithm in this model with query complexity that is independent of the size of the graph, also has a distanceapproximation algorithm with query complexity that is independent of the size of the graph. In this work we focus on boundeddegree and general sparse graphs, and give algorithms for all properties that were shown to have efficient testing algorithms by Goldreich and Ron (Algorithmica, 2002). Specifically, these properties are kedge connectivity, subgraphfreeness (for constant size subgraphs), being a Eulerian graph, and cyclefreeness. A variant of our subgraphfreeness algorithm approximates the size of a minimum vertex cover of a graph in sublinear time. This approximation improves on a recent result of Parnas and Ron (ECCC 2005).
Facility location in sublinear time
 In 32nd International Colloquium on Automata, Languages, and Programming
, 2005
"... Abstract. In this paper we present a randomized constant factor approximation algorithm for the problem of computing the optimal cost of the metric Minimum Facility Location problem, in the case of uniform costs and uniform demands, and in which every point can open a facility. By exploiting the fac ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we present a randomized constant factor approximation algorithm for the problem of computing the optimal cost of the metric Minimum Facility Location problem, in the case of uniform costs and uniform demands, and in which every point can open a facility. By exploiting the fact that we are approximating the optimal cost without computing an actual solution, we give the first algorithm for this problem with running time O(n log 2 n), where n is the number of metric space points. Since the size of the representation of an npoint metric space is Θ(n 2), the complexity of our algorithm is sublinear with respect to the input size. We consider also the general version of the metric Minimum Facility Location problem and we show that there is no o(n 2)time algorithm, even a randomized one, that approximates the optimal solution to within any factor. This result can be generalized to some related problems, and in particular, the cost of minimumcost matching, the cost of bichromatic matching, or the cost of n/2median cannot be approximated in o(n 2)time. 1
Counting Stars and Other Small Subgraphs in Sublinear Time
"... Detecting and counting the number of copies of certain subgraphs (also known as network motifs or graphlets), is motivated by applications in a variety of areas ranging from Biology to the study of the WorldWideWeb. Several polynomialtime algorithms have been suggested for counting or detecting t ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
Detecting and counting the number of copies of certain subgraphs (also known as network motifs or graphlets), is motivated by applications in a variety of areas ranging from Biology to the study of the WorldWideWeb. Several polynomialtime algorithms have been suggested for counting or detecting the number of occurrences of certain network motifs. However, a need for more efficient algorithms arises when the input graph is very large, as is indeed the case in many applications of motif counting. In this paper we design sublineartime algorithms for approximating the number of copies of certain constantsize subgraphs in a graph G. That is, our algorithms do not read the whole graph, but rather query parts of the graph. Specifically, we consider algorithms that may query the degree of any vertex of their choice and may ask for any neighbor of any vertex of their choice. The main focus of this work is on the basic problem of counting the number of length2 paths and more generally on counting the number of stars of a certain size. Specifically, we design an algorithm that, given an approximation parameter 0 < ɛ < 1 and query access to a graph G, outputs an estimate ˆνs such that with high constant probability, (1−ɛ)νs(G) ≤ ˆνs ≤ (1+ɛ)νs(G), where νs(G) denotes the number of stars of size s + 1 in the graph. The expected query ( complexity and { running time of}) the algorithm are O
Approximate Testing of Visual Properties
 Proc. Sixth Int’l Workshop Approximation Algorithms for Combinatorial Optimization Problems
, 2003
"... Abstract. We initiate a study of property testing as applied to visual properties of images. Property testing is a rapidly developing area investigating algorithms that, with a small number of local checks, distinguish objects satisfying a given property from objects which need to be modified signif ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We initiate a study of property testing as applied to visual properties of images. Property testing is a rapidly developing area investigating algorithms that, with a small number of local checks, distinguish objects satisfying a given property from objects which need to be modified significantly to satisfy the property. We study visual properties of discretized images represented by n × n matrices of binary pixel values. We obtain algorithms with query complexity independent of n for several basic properties: being a halfplane, connectedness and convexity. 1
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
"... We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in Rd. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a struct ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in Rd. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + &quot; using only eO(pn poly(1=&quot;)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbors queries.
New Sublinear Methods in the Struggle against Classical Problems
, 2010
"... We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear algorithms. For instance, we obtain a more efficient approximation algorithm for edit distance and distributed algorithms for combinatorial problems on graphs that run in a constant number of communication rounds.
Dynamic Graphs in the SlidingWindow Model
"... We present the first algorithms for processing graphs in the slidingwindow model. The sliding window model, introduced by Datar et al. (SICOMP 2002), has become a popular model for processing infinite data streams in small space when older data items (i.e., those that predate a sliding window cont ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
We present the first algorithms for processing graphs in the slidingwindow model. The sliding window model, introduced by Datar et al. (SICOMP 2002), has become a popular model for processing infinite data streams in small space when older data items (i.e., those that predate a sliding window containing the most recent data items) are considered “stale ” and should implicitly be ignored. While processing massive graph streams is an active area of research, it was hitherto unknown whether it was possible to analyze graphs in the slidingwindow model. We present an extensive set of positive results including algorithms for constructing basic graph synopses like combinatorial sparsifiers and spanners as well as approximating classic graph properties such as the size of a graph matching or minimum spanning tree.
On derandomizing probabilistic sublineartime algorithms
 In Proceedings of the 22nd IEEE conference on computational complexity
, 2007
"... ..."
(Show Context)