Balanced Graph Partitioning

Andreev, Konstantin; Räcke, Harald

doi:10.1007/s00224-006-1350-7

Cited by 330 publications

(188 citation statements)

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“…Such models frequently correspond to different types of graph partitioning problems. Some examples are the use of a balanced partitioning (Andreev and Räcke 2004), minimizing the number or weight of cuts (Reinelt et al 2008; Barnes et al 1988), or by limiting the number of cuts (Reinelt and Wenger 2010). The problem of finding the maximal partitioning of graphs with supply and demand (MPGSD) has shown to be closely related to the maximization of selfadequacy of interconnected microgrids (Jovanovic and Bousselham 2014;Jovanovic et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

2015

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In recent years there has been a growing interest for the problem of the minimal partitioning of graphs with supply and demand, due to its close connection to electrical distribution systems, especially in the context of smartgrids. In this paper we present a new version of the problem which is more suitable for practical applications in modeling such systems. More precisely, the constraint of having a unique supply node in a subgraph (partition) is substituted with a limit on the number of subgraphs and the capacity for each of them. The problem is initially solved by a two stage greedy method. With the goal of further improving the quality of found solutions, a corresponding GRASP and an ant colony optimization algorithm are developed. Due to the novelty of the problem, we include a description of a method for generating test instances with known optimal solutions. In our computational experiments we evaluate the performance of the proposed algorithms on both trees and general graphs. The tests show that the proposed ant colony approach manages to frequently find optimal solutions. It has an average relative error of less than 2 % when compared to known optimal solutions. Moreover, it outperform the GRASP. B Raka Jovanovic

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Section: Introductionmentioning

confidence: 99%

Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

2015

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“…The problem of star decomposition has several applications including scientific computing, scheduling, load balancing and parallel computing [1], important nodes detection for studying the robustness in Peer to Peer social networks [22]. In addition to applications in distributed systems, the decomposition into p-stars can be used also in the field of parallel computing and programming.…”

Section: Introductionmentioning

confidence: 99%

“…{u} = C (v)1 ), else v keeps v.L = {u}. Thus, the next updating of v.inStar must be definitive because the next invitation by executing Rule [I] allows v to invite only a node u with u.inStar = false and |u.L| 1 and only move to be a center node for u (creating p pointers and updating inStar = true) is the Rule [A].…”

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confidence: 98%

“…Note that the rules of the second group require that v.inStar = false.This means that if a node v is agreeing then v cannot execute any rule of this group (since [U3] is disabled).Moreover, only one node can execute an acceptation or an invitation move in the same neighborhood, by checking if the current node v has the smallest v.flag = true within its neighborhood (using predicate smallest(v)).The intuitive idea of SMSD is as follows: each node v which is agreeing for belonging to a p-star has v.inStar = true. Otherwise, v points by v.L at the smallest possible center, defined by C (v)1 . Thus, if a node v has at least p neighbors that point at only v (i.e.…”

mentioning

confidence: 99%

“…The rules of the second group ([A,I]) are responsible for creating and accepting invitations (critical moves). The Rule [A] permits to a node v for accepting invitations from its p neighbors and the Rule [I] for inviting the smallest possible neighbor to be a center node or to∅ where C (v) 1 = ∅ (recall that C (v)1 returns the smallest node in C (v)). Note that the rules of the second group require that v.inStar = false.This means that if a node v is agreeing then v cannot execute any rule of this group (since [U3] is disabled).Moreover, only one node can execute an acceptation or an invitation move in the same neighborhood, by checking if the current node v has the smallest v.flag = true within its neighborhood (using predicate smallest(v)).The intuitive idea of SMSD is as follows: each node v which is agreeing for belonging to a p-star has v.inStar = true.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A new self-stabilizing algorithm for maximal p-star decomposition of general graphs

Neggazi

Haddad

Kheddouci

2015

Information Processing Letters

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Enabling application‐aware flexible graph partition mechanism for parallel graph processing systems

Dong

Zhang

Luo

et al. 2016

Concurrency and Computation

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With the emerging of the large-scale graph data, Pregel-like graph parallel processing systems have been an essential tool to efficiently process the graph data. The first step to use the Pregel-like systems is to partition the graph into multiple blocks and distribute them on multiple machines. The partition strategy plays a significant role in determining the performance because a good partition could both ensure load balance and optimize network communication overhead, and vice versa. However, existing partition strategies fail to meet the requirements because they suffer from the following drawbacks: (1) they ignore the application features and (2) they ignore the multi-application feature in productive environment. To overcome those drawbacks, we proposed the superblock partition strategy, which utilizes the atomic blocks generated by pre-processing of the original graph and could be constructed and re-constructed dynamically according to the submitted applications in real time. The hash-based and clustering-based pre-partition methods are covered in details. The application feature extraction method and heuristic superblock partition algorithm are proposed to construct the superblocks. Experimental results show that the superblock partition strategy could boost the graph processing performance and its partition efficiency also outperforms the hash-based and topology optimal partition strategy. e3849 6 1 of 7 1 [17-19]. The original graph in Figure 1(a) is partitioned into blocks with different partition strategies. The most used partition strategy in existing distributed system is hash based, shown in 1b, where only the hash value of one vertex is considered. The hash-based strategy ensures an even distribution of vertices, which assists to balance the computation load. The hash partition strategy randomly distributes the vertices and causes the neighboring vertices to reside in different blocks, and it may cause network traffic overhead. Some research work, such as [20], is dedicated to solve the problem and limit the inter-machine communication by assigning the topologically connected vertices to the same block. The partition strategy in Figure 1(c) concerns more about network optimization. The connection between each blocks is minimized, which reduces the potential network communication because the vertex sends messages along edges. Compared with Figure 1(c) and d ensures a better load balance because the vertex in each block is of the same number and the worker loading those blocks have the same number of vertices to compute, which is regarded as the topology optimal partition strategy.Although existing partition strategy has partially solved the problems of distributing vertices among multiple workers according to the hash value or topology information, there still exists the following two drawbacks.Firstly, existing partition strategies ignore the application features. State-of-the-art partition strategies focus mainly on hash value or topology information but ignore the application features, which me...

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Balanced Graph Partitioning

Cited by 330 publications

References 12 publications

Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

Partitioning of supply/demand graphs with capacity limitations: an ant colony approach

A new self-stabilizing algorithm for maximal p-star decomposition of general graphs

Enabling application‐aware flexible graph partition mechanism for parallel graph processing systems

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