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Finding small balanced separators
, 2006
"... Let G be an nvertex graph that has a vertex separator of size k that partitions the graph into connected components of size smaller than αn, for some fixed 2/3 ≤ α < 1. Such a separator is called an αseparator. Finding an αseparator of size at most k is NPhard. Moreover, under reasonable comp ..."
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Cited by 11 (0 self)
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our algorithm finds one such separator. For fixed ɛ, the running time of our algorithm is n O(1) 2 O(k) , which is polynomial for k = O(log n). For bounded degree graphs (as well as for the case of finding balanced edge separators), we present a deterministic algorithm with similar running time. Our
On Balanced Separators, Treewidth, and Cycle Rank
"... We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k · ( 1 + log n k, thus refining the previo ..."
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Cited by 1 (1 self)
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We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k · ( 1 + log n k, thus refining
Applications of BalancedSeparator Approximations to Ordering Problems
"... We give the first polynomialtime approximation algorithms for three problems in combinatorial optimization using approximation algorithms for finding balanced separators. The first problem is register sufficiency where, given a computation dag, we are required to find the minimum number of regis ..."
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We give the first polynomialtime approximation algorithms for three problems in combinatorial optimization using approximation algorithms for finding balanced separators. The first problem is register sufficiency where, given a computation dag, we are required to find the minimum number
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 521 (19 self)
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, small balanced separators can be found efficiently. Faithful lowdimensional representations of statistical data allow for meaningful and efficient clustering, which is one of the most basic tasks in patternrecognition. For the (mostly heuristic) methods used
Live Migration of Virtual Machines
 In Proceedings of the 2nd ACM/USENIX Symposium on Networked Systems Design and Implementation (NSDI
, 2005
"... Migrating operating system instances across distinct physical hosts is a useful tool for administrators of data centers and clusters: It allows a clean separation between hardware and software, and facilitates fault management, load balancing, and lowlevel system maintenance. By carrying out the ma ..."
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Cited by 616 (14 self)
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Migrating operating system instances across distinct physical hosts is a useful tool for administrators of data centers and clusters: It allows a clean separation between hardware and software, and facilitates fault management, load balancing, and lowlevel system maintenance. By carrying out
Towards an O ( 3 √ log n)Approximation Algorithm for Balanced Separator
, 907
"... The cBalanced Separator problem is a graphpartitioning problem in which given a graph G, one aims to find a cut of minimum size such that both the sides of the cut have at least cn vertices. In this paper, we present new directions of progress in the cBalanced Separator problem. More specifically ..."
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The cBalanced Separator problem is a graphpartitioning problem in which given a graph G, one aims to find a cut of minimum size such that both the sides of the cut have at least cn vertices. In this paper, we present new directions of progress in the cBalanced Separator problem. More
Vl2: A scalable and flexible data center network
 In SIGCOMM
, 2009
"... To be agile and cost effective, data centers must allow dynamic resource allocation across large server pools. In particular, the data center network should provide a simple flat abstraction: it should be able to take any set of servers anywhere in the data center and give them the illusion that the ..."
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Cited by 443 (12 self)
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that they are plugged into a physically separate, noninterfering Ethernet switch with as many ports as the service needs. To meet this goal, we present VL2, a practical network architecture that scales to support huge data centers with uniform high capacity between servers, performance isolation between services
Expander Flows, Geometric Embeddings and Graph Partitioning
 IN 36TH ANNUAL SYMPOSIUM ON THE THEORY OF COMPUTING
, 2004
"... We give a O( log n)approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)approximation of Leighton and Rao (1988). We use a wellknown semidefinite relaxation with triangle inequality constraints. Central to our analysis is a ..."
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Cited by 309 (18 self)
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We give a O( log n)approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)approximation of Leighton and Rao (1988). We use a wellknown semidefinite relaxation with triangle inequality constraints. Central to our analysis is a
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design alternatives, we discuss their relative merits and we give examples of systems which adopt one approach or the other. The aim is to introduce some order in the complex discipline of designing and understanding faulttolerant distributed systems.
Approximating the exponential, the Lanczos method, and an Õ(m)time spectral algorithm for balanced separator
 IN: PROCEEDINGS OF THE 44TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC
, 2012
"... We give a novel spectral approximation algorithm for the balanced separator problem that, given a graph G, a constant balance b ∈ (0, 1/2], and a parameter γ, either finds an Ω(b)balanced cut of conductance O ( √ γ) in G, or outputs a certificate that all bbalanced cuts in G have conductance at le ..."
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Cited by 10 (3 self)
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We give a novel spectral approximation algorithm for the balanced separator problem that, given a graph G, a constant balance b ∈ (0, 1/2], and a parameter γ, either finds an Ω(b)balanced cut of conductance O ( √ γ) in G, or outputs a certificate that all bbalanced cuts in G have conductance
Results 1  10
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