Results 11  20
of
48
When Clusters Meet Partitions: A New Density Objective for Circuit Decomposition
 In Proc. European Design and Test Conf
, 1994
"... Recent research on multiway partitioning has focused on the minimum cut [20, 26, 27] or generalized ratio cut [28, 29, 5] cost metrics. At the same time, clustering research has focused on such objectives as kl connectivity [12], DS metric [6], or cliquefinding [8]. In this paper, we make the b ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
Recent research on multiway partitioning has focused on the minimum cut [20, 26, 27] or generalized ratio cut [28, 29, 5] cost metrics. At the same time, clustering research has focused on such objectives as kl connectivity [12], DS metric [6], or cliquefinding [8]. In this paper, we make the basic observation that cut objectives in partitioning, and density objectives in clustering, are fundamentally incompatible. Moreover, for multiway decomposition applications (e.g., decomposing a system onto multiple FPGA chips), the two approaches fail to smoothly "meet in the middle". We present a new measure of multiway circuit decomposition, based on a sum of densities objective. Here, the density of a subgraph is the ratio of the number of edges to the number of nodes in the subgraph. In that we feel that this is a natural measure of circuit decomposition (indeed, arguably more natural than ratio cut for a variety of applications), our new objective can perhaps be viewed in the same sp...
An indepth study of graph partitioning measures for perceptual organization
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... In recent years, one of the effective engines for perceptual organization of lowlevel image features is based on the partitioning of a graph representation that captures Gestalt inspired local structures, such as similarity, proximity, continuity, parallelism, and perpendicularity, over the lowle ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
In recent years, one of the effective engines for perceptual organization of lowlevel image features is based on the partitioning of a graph representation that captures Gestalt inspired local structures, such as similarity, proximity, continuity, parallelism, and perpendicularity, over the lowlevel image features. Mainly motivated by computational efficiency considerations, this graph partitioning process is usually implemented as a recursive bipartitioning process, where, at each step, the graph is broken into two parts based on a partitioning measure. We concentrate on three such measures, namely, the minimum [41], average [28], and normalized [32] cuts. The minimum cut partition seeks to minimize the total link weights cut. The average cut measure is proportional to the total link weight cut, normalized by the sizes of the partitions. The normalized cut measure is normalized by the product of the total connectivity (valencies) of the nodes in each partition. We provide theoretical and empirical insight into the nature of the three partitioning measures in terms of the underlying image statistics. In particular, we consider for what kinds of image statistics would optimizing a measure, irrespective of the particular algorithm used, result in correct partitioning. Are the quality of the groups significantly different for each cut measure? Are there classes of images for which grouping by partitioning does not work well? Another question of interest is if the recursive bipartitioning strategy can separate out groups corresponding toK objects from each other. In the analysis, we draw from probability theory and the rich body of work on stochastic ordering of random variables. Our major conclusion is that optimization of none of the three measures is guaranteed to result in the correct partitioning ofK objects, in the strict stochastic order sense, for all image statistics. Qualitatively speaking, under very restrictive conditions, when the average interobject feature affinity is very weak
Greedy splitting algorithms for approximating multiway partition problems
 Math. Programming
, 2005
"... Abstract. Given a system (V, T, f, k), where V is a finite set, T ⊆ V, f: 2 V → R is a submodular function and k ≥ 2 is an integer, the general multiway partition problem (MPP) asks to find a kpartition P = {V1, V2,..., Vk} of V that satisfies Vi ∩T � = ∅ for all i and minimizes f(V1)+f(V2)+ · · ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Given a system (V, T, f, k), where V is a finite set, T ⊆ V, f: 2 V → R is a submodular function and k ≥ 2 is an integer, the general multiway partition problem (MPP) asks to find a kpartition P = {V1, V2,..., Vk} of V that satisfies Vi ∩T � = ∅ for all i and minimizes f(V1)+f(V2)+ · · ·+f(Vk), where P is a kpartition of V if (i) Vi � = ∅, (ii) Vi ∩ Vj = ∅, i � = j, and (iii) V1 ∪ V2 ∪ · · · ∪ Vk = V hold. MPP formulation captures a generalization in submodular systems of many NPhard problems such as kway cut, multiterminal cut, target split and their generalizations in hypergraphs. This paper presents a simple and unified framework for developing and analyzing approximation algorithms for various MPPs. Key words. approximation algorithm – hypergraph partition – kway cut – multiterminal cut – multiway partition problem – submodular function 1.
Cut problems in graphs with a budget constraint
 IN PROC. 7TH LATIN AMERICAN THEORETICAL INFORMATICS SYMPOSIUM
, 2006
"... We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the kCut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the kcut problems we provide constant factor approximation algorithms ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
(Show Context)
We study budgeted variants of classical cut problems: the Multiway Cut problem, the Multicut problem, and the kCut problem, and provide approximation algorithms for these problems. Specifically, for the budgeted multiway cut and the kcut problems we provide constant factor approximation algorithms. We show that the budgeted multicut problem is at least as hard to approximate as the sparsest cut problem, and we provide a bicriteria approximation algorithm for it.
Improving performance and availability of services hosted on IaaS clouds with structural constraintaware virtual machine placement
 in IEEE SCC
, 2011
"... Abstract—The increasing popularity of modern virtualizationbased datacenters continues to motivate both industry and academia to provide answers to a large variety of new and challenging questions. In this paper we aim to answer focusing on one such question: how to improve performance and availabil ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
Abstract—The increasing popularity of modern virtualizationbased datacenters continues to motivate both industry and academia to provide answers to a large variety of new and challenging questions. In this paper we aim to answer focusing on one such question: how to improve performance and availability of services hosted on IaaS clouds. Our system, structural constraintaware virtual machine placement (SCAVP), supports three types of constraints: demand, communication and availability. We formulate SCAVP as an optimization problem and show its hardness. We design a hierarchical placement approach with four approximation algorithms that efficiently solves the SCAVP problem for large problem sizes. We provide a formal model for the application (to better understand structural constraints) and the datacenter (to effectively capture capabilities), and use the two models as inputs to the placement problem. We evaluate SCAVP in a simulated environment to illustrate the efficiency and importance of the proposed approach.
Approximation and Hardness Results for Label Cut and Related Problems
"... We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t. We give the first nontrivial approximation and hardness results for the Label Cut problem. Firstly, we present an O ( √ m)approximation algorithm for the Label Cut problem, where m is the number of edges in the input graph. Secondly, we show that it is NPhard to approximate Label Cut within 2 log1−1 / log logc n n for any constant c < 1/2, where n is the input length of the problem. Thirdly, our techniques can be applied to other previously considered optimization problems. In particular we show that the Minimum Label Path problem has the same approximation hardness as that of Label Cut, simultaneously improving and unifying two known hardness results for this problem which were previously the best (but incomparable due to different complexity assumptions). 1
Scheduling balanced taskgraphs to LogPmachines
 PARALLEL COMPUTING
, 2000
"... This article discusses algorithms for scheduling task graphs G =(V, E, ) to LogPmachines. These algorithms depend on the granularity of G, i.e. on the ratio of computation (v) and communication times in the LogP cost model, and on the structure of G. We de ne a class of coarse grained task graphs t ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
This article discusses algorithms for scheduling task graphs G =(V, E, ) to LogPmachines. These algorithms depend on the granularity of G, i.e. on the ratio of computation (v) and communication times in the LogP cost model, and on the structure of G. We de ne a class of coarse grained task graphs that can be scheduled with a performance guarantee of 4 Topt(G), where Topt(G) is the time required for the optimal makespan. Furthermore, we define a class of ne grained task graphs that can be scheduled with a performance guarantee approaching 4 Topt(G) for increasing problem sizes. The discussed classes of task graphs cover algorithms such as Fast Fourier Transformation, Stencil Computations to solve partial differential equations, matrix multiplication etc.
The Steiner kcut problem
, 2006
"... We consider the Steiner kcut problem which generalizes both the kcut problem and the multiway cut problem. The Steiner kcut problem is defined as follows. Given an edgeweighted undirected graph G =(V,E), a subset of vertices X ⊆ V called terminals, and an integer k ≤X, the objective is to find ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We consider the Steiner kcut problem which generalizes both the kcut problem and the multiway cut problem. The Steiner kcut problem is defined as follows. Given an edgeweighted undirected graph G =(V,E), a subset of vertices X ⊆ V called terminals, and an integer k ≤X, the objective is to find a minimum weight set of edges whose removal results in k disconnected components, each of which contains at least one terminal. We give two approximation algorithms for the problem: a greedy (2 − 2 k)approximation based on Gomory–Hu trees, and a (2 −
Multicommodity Flows and Approximation Algorithms
, 1994
"... This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a groundbreaking work Leighton and Rao [34] showed an approximate maxflow mincut theorem for uniform multicommodity flow and used this to obtain an approximation ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a groundbreaking work Leighton and Rao [34] showed an approximate maxflow mincut theorem for uniform multicommodity flow and used this to obtain an approximation algorithm for the flux of a graph. We consider the multicommodity flow problem in which the object is to maximize the sum of the flows routed and prove the following approximate maxflow minmulticut theorem minmulticut O(log k) maxflow minmulticut where k is the number of commodities. Our proof is based on a rounding technique from [34]. Further, we show that this theorem is tight. For a multicommodity flow instance with specified demands, the ratio of the maximum concurrent flow to the sparsest cut was shown to be bounded by O(log 2 k) [30, 57, 17, 47]. We use ideas from our proof of the approximate maxflow minmulticut theorem and a geometric scaling technique from [1] to provi...
A multiagent algorithm for graph partitioning
"... The kcut problem is an NPcomplete problem which consists of finding a partition of a graph into k balanced parts such that the number of cut edges is minimized. Different algorithms have been proposed for this problem based on heuristic, geometrical and evolutionary methods. In this paper we prese ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
The kcut problem is an NPcomplete problem which consists of finding a partition of a graph into k balanced parts such that the number of cut edges is minimized. Different algorithms have been proposed for this problem based on heuristic, geometrical and evolutionary methods. In this paper we present a new simple multiagent algorithm, ants, and we test its performance with standard graph benchmarks. The results show that this method can outperform several current methods while it is very simple to implement.