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A new diffusionbased multilevel algorithm for computing graph partitions of very high quality
 In Proc. 22nd IPDPS
, 2008
"... Abstract. Graph partitioning requires the division of a graph's vertex set into k equally sized subsets s. t. some objective function is optimized. Highquality partitions are important for many applications, whose objective functions are often NPhard to optimize. Most stateoftheart graph p ..."
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Cited by 33 (10 self)
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Abstract. Graph partitioning requires the division of a graph's vertex set into k equally sized subsets s. t. some objective function is optimized. Highquality partitions are important for many applications, whose objective functions are often NPhard to optimize. Most stateoftheart graph partitioning libraries use a variant of the KernighanLin (KL) heuristic within a multilevel framework. While these libraries are very fast, their solutions do not always meet all user requirements. Moreover, due to its sequential nature, KL is not easy to parallelize. Its use as a load balancer in parallel numerical applications therefore requires complicated adaptations. That is why we developed previously an inherently parallel algorithm, called BubbleFOS/C (Meyerhenke et al., IPDPS'06), which optimizes partition shapes by a diffusive mechanism. However, it is too slow for practical use, despite its high solution quality. In this paper, besides proving that BubbleFOS/C converges towards a local optimum of a potential function, we develop a much faster method for the improvement of partitionings. This faster method called TruncCons is based on a different diffusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism. By coupling TruncCons with BubbleFOS/C in a multilevel framework based on two different hierarchy construction methods, we obtain our new graph
RELAXATIONBASED COARSENING AND MULTISCALE GRAPH ORGANIZATION
"... In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the “closeness” between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar ..."
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Cited by 14 (8 self)
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In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the “closeness” between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at each coarser level. We demonstrate the use of this measure in multiscale methods for several important combinatorial optimization problems and discuss the multiscale graph organization.
Multilevel algorithms for linear ordering problems
, 2007
"... Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,..., n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a ..."
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Cited by 12 (7 self)
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Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2,..., n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a variety of lineartime algorithms for these problems inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. The experimental result for four such problems turned out to be better than every known result in almost all cases, while the short running time of the algorithms enables testing very large graphs.
Comparison of coarsening schemes for multilevel graph partitioning
 in: Learning and Intelligent Optimization: Third International Conference, LION 3. Selected Papers
, 2009
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Graph partitioning and disturbed diffusion
 Parallel Computing
, 2009
"... The N Phard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph’s vertex set into P equally sized subsets such that some objective function is optimized. Stateoftheart libraries addressing this problem show several ..."
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Cited by 10 (7 self)
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The N Phard graph partitioning problem is an important subtask in load balancing and many other applications. It requires the division of a graph’s vertex set into P equally sized subsets such that some objective function is optimized. Stateoftheart libraries addressing this problem show several deficiencies: they are hard to parallelize, focus on small edgecuts instead of few boundary vertices, and often produce disconnected partitions. This work introduces our novel graph partitioning and repartitioning heuristic BubbleFOS/C. In contrast to other libraries, BubbleFOS/C does not try to minimize the edgecut explicitly, but focuses instead implicitly on good partition shapes. The shapes are optimized by diffusion processes that are embedded into an iterative framework. This approach incorporates a high degree of parallelism. Besides describing the evolution process that led to the new diffusion scheme FOS/C used by BubbleFOS/C, we reveal some of FOS/C’s properties and propose a number of enhancements for a fast and reliable implementation. Our experiments, in which we compare sequential and parallel BubbleFOS/C implementations to the stateoftheart libraries Metis and Jostle, reveal that our new heuristic generates highquality solutions.
A Multilevel Algorithm for the Minimum 2sum Problem
"... In this paper we introduce a direct motivation for solving the minimum 2sum problem, for which we present a lineartime algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short runn ..."
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Cited by 6 (4 self)
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In this paper we introduce a direct motivation for solving the minimum 2sum problem, for which we present a lineartime algorithm inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. Our results turned out to be better than previous results, while the short running time of the algorithm enabled experiments with very large graphs. We thus introduce a new benchmark for the minimum 2sum problem which contains 66 graphs of various characteristics. In addition, we propose the straightforward use of a part of our algorithm as a powerful local reordering method for any other (than multilevel) framework.
Decorous lower bounds for minimum linear arrangement. Working paper
, 2009
"... Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the su ..."
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Cited by 5 (2 self)
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Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this paper, we propose a linearprogramming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances.
E.: Exploremaps: Efficient construction and ubiquitous exploration of panoramic view graphs of complex 3d environments. Computer Graphics Forum 33(2
 Proc. Eurographics 2014
, 2014
"... Figure 1: We automatically transform a generic renderable model (left) into a simple graph representation named ExploreMaps (center), where nodes are nicely placed point of views that cover the visible model surface and arcs are smooth paths between neighboring probes. The representation is exploite ..."
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Cited by 4 (2 self)
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Figure 1: We automatically transform a generic renderable model (left) into a simple graph representation named ExploreMaps (center), where nodes are nicely placed point of views that cover the visible model surface and arcs are smooth paths between neighboring probes. The representation is exploited for providing visual indexes for the 3D scene and for supporting, even on lowpowered mobile devices, interactive photorealistic exploration based on precomputed imagery (right). We introduce a novel efficient technique for automatically transforming a generic renderable 3D scene into a simple graph representation named ExploreMaps, where nodes are nicely placed point of views, called probes, and arcs are smooth paths between neighboring probes. Each probe is associated with a panoramic image enriched with preferred viewing orientations, and each path with a panoramic video. Our GPUaccelerated unattended construction pipeline distributes probes so as to guarantee coverage of the scene while accounting for perceptual criteria before finding smooth, good looking paths between neighboring probes. Images and videos are precomputed at construction time with offline photorealistic rendering engines, providing a convincing 3D visualization beyond the limits of current realtime graphics techniques. At runtime, the graph is exploited both for creating automatic scene indexes and movie previews of complex scenes and for supporting interactive exploration through a lowDOF assisted navigation interface and the visual indexing of the scene provided by the selected viewpoints. Due to negligible CPU overhead and very limited use of GPU functionality, realtime performance is achieved on emerging webbased environments based on WebGL even on lowpowered mobile devices.
Memetic algorithms for the MinLA problem
 Lecture Notes in Computer Science
"... Abstract. This paper presents a new Memetic Algorithm designed to compute near optimal solutions for the MinLA problem. It incorporates a highly specialized crossover operator, a fast MinLA heuristic used to create the initial population and a local search operator based on a fine tuned Simulated An ..."
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Cited by 3 (2 self)
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Abstract. This paper presents a new Memetic Algorithm designed to compute near optimal solutions for the MinLA problem. It incorporates a highly specialized crossover operator, a fast MinLA heuristic used to create the initial population and a local search operator based on a fine tuned Simulated Annealing algorithm. Its performance is investigated through extensive experimentation over well known benchmarks andcomparedwithotherstateoftheartalgorithms. Key words: Memetic Algorithms, Linear Arrangement, Heuristics. 1
Improving Random Walk Performance
"... Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different onedimens ..."
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Cited by 2 (0 self)
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Random walk simulation is employed in many experimental algorithmic applications. Efficient execution on modern computer architectures demands that the random walk be implemented to exploit data locality for improving the cache performance. In this research, we demonstrate how different onedimensional data reordering functionals can be used as a preprocessing step for speeding the random walk runtime.