Special Issue "Graph Partitioning: Theory, Engineering, and Applications"

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 June 2019).

Special Issue Editors

Dr. Christian Schulz
Website
Guest Editor
Faculty of Computer Science, Research Group Theory and Applications of Algorithms, University of Vienna, 1010 Vienna, Austria
Interests: graph partitioning; algorithm engineering; parallel algorithms; big data
Dr. Darren Strash
Website
Guest Editor
Department of Computer Science, Hamilton College, Clinton, NY 13323, USA
Interests: theoretical computer science; combinatorial optimization; algorithm engineering; geometric and graph algorithms
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit your latest research in the area of graph partitioning to this Special Issue, Graph Partitioning: Theory, Engineering, and Applications. All facets of graph partitioning will be considered, including shared-memory parallel and distributed algorithms, streaming algorithms, exact algorithms, approximation algorithms, local search, genetic algorithms, metaheuristics, hardness results, parameterized algorithms, variations in objective functions, and alternate partitioning primitives (such as edge partitioning) or process mapping algorithms. High-quality papers are solicited to address both the theoretical and practical issues of graph partitioning. Submissions on graph partitioning’s impact on existing applications, and the introduction of new applications with experiments are highly encouraged.

Dr. Christian Schulz
Dr. Darren Strash
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph partitioning
  • edge partitioning
  • exact algorithms
  • approximate algorithms
  • partitioning heuristics and metaheuristics
  • evolutionary algorithms
  • complexity of partitioning algorithms
  • algorithms for multi-objective partitioning
  • partitioning algorithms for distributed processing
  • engineering efficient graph partitioners
  • shared-memory algorithms
  • distributed algorithms

Published Papers (4 papers)

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Research

Open AccessArticle
Correspondence between Multilevel Graph Partitions and Tree Decompositions
Algorithms 2019, 12(9), 198; https://doi.org/10.3390/a12090198 - 17 Sep 2019
Abstract
We present a mapping between rooted tree decompositions and node separator based multilevel graph partitions. Significant research into both tree decompositions and graph partitions exists. We hope that our result allows for an easier knowledge transfer between the two research avenues. Full article
(This article belongs to the Special Issue Graph Partitioning: Theory, Engineering, and Applications)
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Open AccessArticle
Faster and Better Nested Dissection Orders for Customizable Contraction Hierarchies
Algorithms 2019, 12(9), 196; https://doi.org/10.3390/a12090196 - 16 Sep 2019
Cited by 3
Abstract
Graph partitioning has many applications. We consider the acceleration of shortest path queries in road networks using Customizable Contraction Hierarchies (CCH). It is based on computing a nested dissection order by recursively dividing the road network into parts. Recently, with FlowCutter and Inertial [...] Read more.
Graph partitioning has many applications. We consider the acceleration of shortest path queries in road networks using Customizable Contraction Hierarchies (CCH). It is based on computing a nested dissection order by recursively dividing the road network into parts. Recently, with FlowCutter and Inertial Flow, two flow-based graph bipartitioning algorithms have been proposed for road networks. While FlowCutter achieves high-quality results and thus fast query times, it is rather slow. Inertial Flow is particularly fast due to the use of geographical information while still achieving decent query times. We combine the techniques of both algorithms to achieve more than six times faster preprocessing times than FlowCutter and even faster queries on the Europe road network. We show that, using 16 cores of a shared-memory machine, this preprocessing needs four minutes. Full article
(This article belongs to the Special Issue Graph Partitioning: Theory, Engineering, and Applications)
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Open AccessArticle
Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics
Algorithms 2019, 12(9), 187; https://doi.org/10.3390/a12090187 - 07 Sep 2019
Cited by 1
Abstract
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have [...] Read more.
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime. Full article
(This article belongs to the Special Issue Graph Partitioning: Theory, Engineering, and Applications)
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Open AccessArticle
Distributed Balanced Partitioning via Linear Embedding
Algorithms 2019, 12(8), 162; https://doi.org/10.3390/a12080162 - 10 Aug 2019
Cited by 3
Abstract
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, for example, in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to [...] Read more.
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, for example, in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to certain suboptimality from the interaction among different pieces. In other cases, links between different parts may show up in the running time and/or network communications cost, hence the desire to have small cut size. We study a distributed balanced-partitioning problem where the goal is to partition the vertices of a given graph into k pieces so as to minimize the total cut size. Our algorithm is composed of a few steps that are easily implementable in distributed computation frameworks such as MapReduce. The algorithm first embeds nodes of the graph onto a line, and then processes nodes in a distributed manner guided by the linear embedding order. We examine various ways to find the first embedding, for example, via a hierarchical clustering or Hilbert curves. Then we apply four different techniques including local swaps, and minimum cuts on the boundaries of partitions, as well as contraction and dynamic programming. As our empirical study, we compare the above techniques with each other, and also to previous work in distributed graph algorithms, for example, a label-propagation method, FENNEL and Spinner. We report our results both on a private map graph and several public social networks, and show that our results beat previous distributed algorithms: For instance, compared to the label-propagation algorithm, we report an improvement of 15–25% in the cut value. We also observe that our algorithms admit scalable distributed implementation for any number of partitions. Finally, we explain three applications of this work at Google: (1) Balanced partitioning is used to route multi-term queries to different replicas in Google Search backend in a way that reduces the cache miss rates by ≈ 0.5 % , which leads to a double-digit gain in throughput of production clusters. (2) Applied to the Google Maps Driving Directions, balanced partitioning minimizes the number of cross-shard queries with the goal of saving in CPU usage. This system achieves load balancing by dividing the world graph into several “shards”. Live experiments demonstrate an ≈ 40 % drop in the number of cross-shard queries when compared to a standard geography-based method. (3) In a job scheduling problem for our data centers, we use balanced partitioning to evenly distribute the work while minimizing the amount of communication across geographically distant servers. In fact, the hierarchical nature of our solution goes well with the layering of data center servers, where certain machines are closer to each other and have faster links to one another. Full article
(This article belongs to the Special Issue Graph Partitioning: Theory, Engineering, and Applications)
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