Results 1  10
of
194
Network Coding for Distributed Storage Systems
 In Proc. of IEEE INFOCOM
, 2007
"... Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peertopeer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, ..."
Abstract

Cited by 83 (9 self)
 Add to MetaCart
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peertopeer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an erasure coded system, a common practice to repair from a node failure is for a new node to download subsets of data stored at a number of surviving nodes, reconstruct a lost coded block using the downloaded data, and store it at the new node. We show that this procedure is suboptimal. We introduce the notion of regenerating codes, which allow a new node to download functions of the stored data from the surviving nodes. We show that regenerating codes can significantly reduce the repair bandwidth. Further, we show that there is a fundamental tradeoff between storage and repair bandwidth which we theoretically characterize using flow arguments on an appropriately constructed graph. By invoking constructive results in network coding, we introduce regenerating codes that can achieve any point in this optimal tradeoff. I.
Identification of peer effects through social networks
 Journal of Econometrics
, 2009
"... We provide new results regarding the identification of peer effects. We consider an extended version of the linearinmeans model where each individual has his own specific reference group. Interactions are thus structured through a social network. We assume that correlated unobservables are either ..."
Abstract

Cited by 54 (4 self)
 Add to MetaCart
We provide new results regarding the identification of peer effects. We consider an extended version of the linearinmeans model where each individual has his own specific reference group. Interactions are thus structured through a social network. We assume that correlated unobservables are either absent, or treated as fixed effects at the component level. In both cases, we provide easytocheck necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. Monte Carlo simulations provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of social effects. Our approach generalizes a number of previous results due to Manski (1993), Moffitt (2001), and Lee (2007).
Necessary and sufficient graphical conditions for formation control of unicycles,” technical report, http://www.control.utoronto.ca/people/profs/francis/publications.html
"... Abstract–The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the ..."
Abstract

Cited by 53 (0 self)
 Add to MetaCart
Abstract–The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements. Index Terms–Multiagent system, distributed control, nonholonomic mobile robots. I.
A framework for representing reticulate evolution
 Ann. Combin
, 2004
"... Abstract. Acyclic directed graphs (ADGs) are increasingly being viewed as more appropriate for representing certain evolutionary relationships, particularly in biology, than rooted trees. In this paper, we develop a framework for the analysis of these graphs which we call hybrid phylogenies. We are ..."
Abstract

Cited by 35 (6 self)
 Add to MetaCart
Abstract. Acyclic directed graphs (ADGs) are increasingly being viewed as more appropriate for representing certain evolutionary relationships, particularly in biology, than rooted trees. In this paper, we develop a framework for the analysis of these graphs which we call hybrid phylogenies. We are particularly interested in the problem whereby one is given a set of phylogenetic trees and wishes to determine a hybrid phylogeny that ‘embeds ’ each of these trees and which requires the smallest number of hybridisation events. We show that this quantity can be greatly reduced if additional species are involved, and investigate other combinatorial aspects of this and related questions. 1.
An Extended Class of Instrumental Variables for the Estimation of Causal Effects
 UCSD DEPT. OF ECONOMICS DISCUSSION PAPER
, 1996
"... This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regresso ..."
Abstract

Cited by 32 (13 self)
 Add to MetaCart
This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest.
Network Analysis, Complexity, and Brain Function
 COMPLEXITY
, 2003
"... Throughout the early history of neurology and neuroscience, most theoretical accounts of brain function have emphasized either aspects of localization or distributed properties [1]. Instead, modern views focus extensively on the structure and dynamics of largescale neuronal networks, especially tho ..."
Abstract

Cited by 20 (1 self)
 Add to MetaCart
Throughout the early history of neurology and neuroscience, most theoretical accounts of brain function have emphasized either aspects of localization or distributed properties [1]. Instead, modern views focus extensively on the structure and dynamics of largescale neuronal networks, especially those of the cerebral cortex and associated thalamocortical
Embedding large subgraphs into dense graphs
"... Abstract. What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac’s theorem on Hamilton cycles and Tutte’s theorem on perfect matchings. Perfect matchings are generalized by perfect Fpackings, where instead o ..."
Abstract

Cited by 19 (12 self)
 Add to MetaCart
Abstract. What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac’s theorem on Hamilton cycles and Tutte’s theorem on perfect matchings. Perfect matchings are generalized by perfect Fpackings, where instead of covering all the vertices of G by disjoint edges, we want to cover G by disjoint copies of a (small) graph F. It is unlikely that there is a characterization of all graphs G which contain a perfect Fpacking, so as in the case of Dirac’s theorem it makes sense to study conditions on the minimum degree of G which guarantee a perfect Fpacking. The Regularity lemma of Szemerédi and the Blowup lemma of Komlós, Sárközy and Szemerédi have proved to be powerful tools in attacking such problems and quite recently, several longstanding problems and conjectures in the area have been solved using these. In this survey, we give an outline of recent progress (with our main emphasis on Fpackings, Hamiltonicity problems and tree embeddings) and describe some of the methods involved.
Minimum Cost and List Homomorphisms to Semicomplete Digraphs
 Discrete Appl. Math
"... For digraphs D and H, a mapping f: V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). Let H be a fixed directed or undirected graph. The homomorphism problem for H asks whether a directed or undirected graph input digraph D admits a homomorphism to H. The list homomorphis ..."
Abstract

Cited by 19 (9 self)
 Add to MetaCart
For digraphs D and H, a mapping f: V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). Let H be a fixed directed or undirected graph. The homomorphism problem for H asks whether a directed or undirected graph input digraph D admits a homomorphism to H. The list homomorphism problem for H is a generalization of the homomorphism problem for H, where every vertex x ∈ V (D) is assigned a set Lx of possible colors (vertices of H). The following optimization version of these decision problems was introduced in [16], where it was motivated by a realworld problem in defence logistics. Suppose we are given a pair of digraphs D, H and a positive cost ci(u) for each u ∈ V (D) and i ∈ V (H). The cost of a homomorphism f of D to H is � u∈V (D) cf(u)(u). For a fixed digraph H, the minimum cost homomorphism problem for H, MinHOMP(H), is stated as follows: For an input digraph D and costs ci(u) for each u ∈ V (D) and i ∈ V (H), verify whether there is a homomorphism of D to H and, if it exists, find
Almost 2SAT is fixedparameter tractable
 Journal of Computer and System Sciences
"... Abstract. We consider the following problem. Given a 2CNF formula, is it possible to remove at most k clauses so that the resulting 2CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer Science under the names ’Almost 2SAT’, ’Allbutk 2SAT’ ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
Abstract. We consider the following problem. Given a 2CNF formula, is it possible to remove at most k clauses so that the resulting 2CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer Science under the names ’Almost 2SAT’, ’Allbutk 2SAT’, ’2CNF deletion’, ’2SAT deletion’. The status of fixedparameter tractability of this problem is a longstanding open question in the area of Parameterized Complexity. We resolve this open question by proposing an algorithm which solves this problem in O(15 k ∗ k ∗ m 3) and thus we show that this problem is fixedparameter tractable. 1
Parameterized algorithms for feedback set problems and their duals in tournaments
 Theoretical Computer Science
, 2006
"... The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournamen ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions. We also address the parametric dual problems which are also natural optimization problems. We show that they are fixed parameter tractable not just in tournaments but in oriented directed graphs (where there is at most one directed arc between a pair of vertices). More specifically, the dual problem we show fixed parameter tractable are: Given an oriented directed graph, is there a subset of k vertices (arcs) that forms an acyclic directed subgraph of the graph? Our main results include: • an O((2.4143) k n ω) 1 algorithm for weighted feedback vertex set problem, and an O((2.415) k n ω) algorithm for weighted feedback arc set problem in tournaments; • an O((e2 k /k) k k 2 + min{m lg n,n 2}) algorithm for the dual of feedback vertex set problem (maximum vertex induced acyclic graph) in oriented directed graphs, and an O(4 k k +m) algorithm for the dual of feedback arc set problem (maximum arc induced acyclic graph) in general directed graphs. We also show that the dual of feedback vertex set is W[1]−hard in general directed graphs and the feedback arc set problem is fixed parameter tractable in dense directed graphs. Our results are the first non trivial results for these problems. Key words: tournaments, feedback vertex set, feedback arc set, parameterized complexity 1 ω is the exponent of the best matrix multiplication algorithm. Preprint submitted to Elsevier Science 12 May 2005 1