Graph partitioning is used to solve the problem of distributing computations to a number of processors, in order to improve the performance of time consuming applications in parallel environments. A common approach to solve this problem is based on a multilevel framework, where the graph is firstly coarsened to a smaller instance and then it is partitioned in a number of parts using recursive bisection (RB) based methods. However, in applications where initial fixed vertices are used to model additional constraints of the problem, RB based methods often fail to produce partitions of good quality. In this paper, we propose a new direct k-way greedy graph growing algorithm, called KGGGP, that overcomes this issue and succeeds to produce partition with better quality than RB while respecting the constraint of fixed vertices. In the experimental section, we present results which compare KGGGP against state-of-theart methods for graphs available from the popular DIMACS'10 collection.
The field of network science is a highly interdisciplinary area; for the empirical analysis of network data, it draws algorithmic methodologies from several research fields. Hence, research procedures and descriptions of the technical results often differ, sometimes widely. In this paper we focus on methodologies for the experimental part of algorithm engineering for network analysis -an important ingredient for a research area with empirical focus. More precisely, we unify and adapt existing recommendations from different fields and propose universal guidelines -including statistical analyses -for the systematic evaluation of network analysis algorithms. This way, the behavior of newly proposed algorithms can be properly assessed and comparisons to existing solutions become meaningful. Moreover, as the main technical contribution, we provide SimexPal, a highly automated tool to perform and analyze experiments following our guidelines. To illustrate the merits of SimexPal and our guidelines, we apply them in a case study: we design, perform, visualize and evaluate experiments of a recent algorithm for approximating betweenness centrality, an important problem in network analysis. In summary, both our guidelines and SimexPal shall modernize and complement previous efforts in experimental algorithmics; they are not only useful for network analysis, but also in related contexts.
In this paper we propose a new method to enhance a mapping µ(·) of a parallel application's computational tasks to the processing elements (PEs) of a parallel computer. The idea behind our method TIMER is to enhance such a mapping by drawing on the observation that many topologies take the form of a partial cube. This class of graphs includes all rectangular and cubic meshes, any such torus with even extensions in each dimension, all hypercubes, and all trees.Following previous work, we represent the parallel application and the parallel computer by graphs G a = (V a , E a ) and G p = (V p , E p ). G p being a partial cube allows us to label its vertices, the PEs, by bitvectors such that the cost of exchanging one unit of information between two vertices u p and p of G p amounts to the Hamming distance between the labels of u p and p .By transferring these bitvectors from V p to V a via µ −1 (·) and extending them to be unique on V a , we can enhance µ(·) by swapping labels of V a in a new way. Pairs of swapped labels are local w. r. t. the PEs, but not w. r. t. G a . Moreover, permutations of the bitvectors' entries give rise to a plethora of hierarchies on the PEs. Through these hierarchies we turn TIMER into a hierarchical method for improving µ(·) that is complementary to state-of-the-art methods for computing µ(·) in the first place.In our experiments we use TIMER to enhance mappings of complex networks onto rectangular meshes and tori with 256 and 512 nodes, as well as hypercubes with 256 nodes. It turns out that common quality measures of mappings derived from state-of-the-art algorithms can be improved considerably.
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