Graph Partitioning-Based Coordination Methods for Large-Scale Multidisciplinary Design Optimization Problems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97127/1/AIAA2012-5522.pd

Minimum Bisection is fixed parameter tractable

In the classic Minimum Bisection problem we are given as input a graph G and an integer k. The task is to determine whether there is a partition of V (G) into two parts A and B such that ||A | − |B| | ≤ 1 and there are at most k edges with one endpoint in A and the other in B. In this paper we give an algorithm for Minimum Bisection with running time O(2 O(k3) n 3 lo

A cluster algorithm for graphs

A cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The MCL~algorithm simulates flow in $G$ by first identifying $G$ in a canonical way with a Markov graph $G_1$. Flow is then alternatingly expanded and contracted, leading to a row of Markov Graphs G_{(i). Flow expansion corresponds with taking the~k^{th~power of a stochastic matrix, where~$kinN$. Flow contraction corresponds with a parametrized operator~$Gamma_r$, $rgeq 0$, which maps the set of (column) stochastic matrices onto itself. The image~$Gamma_r M$ is obtained by raising each entry in~$M$ to the~r^{th~power and rescaling each column to have sum~$1$ again. The heuristic underlying this approach is the expectation that flow between dense regions which are sparsely connected will evaporate. The invariant limits of the process are easily derived and in practice the process converges very fast to such a limit, the structure of which has a generic interpretation as an overlapping clustering of the graph~$G$. Overlap is limited to cases where the input graph has a symmetric structure inducing it. The contraction and expansion parameters of the MCL~process influence the granularity of the output. The algorithm is space and time efficient and lends itself to drastic scaling. This report describes the MCL~algorithm and process, convergence towards equilibrium states, interpretation of the states as clusterings, and implementation and scalability. The algorithm is introduced by first considering several related proposals towards graph clustering, of both combinatorial and probabilistic nature. Revised version of the report~[1]. A more mathematically oriented account on the MCL~process is given in~[2], establishing that under certain weak conditions the iterands of the MCL~process posses structure admitting a cluster interpretation. Various experiments conducted on a wide range of test-graphs are described in~[3]. The latter report also describes a generic graph clustering performance measure and a distance defined on the space of partitions. The work was carried out under project INS-3.2, Concept Building from Key-Phrases in Scientific Documents and Bottom Up Classification Methods in Mathematics. [1] A new cluster algorithm for graphs. Technical report INS-R9814, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam, 1998. [2] A stochastic uncoupling process for graphs. Technical report INS-R0011, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam, 2000. [3] Performance criteria for graph clustering and Markov cluster experiments. Technical report INS-R0012, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam, 2000

High performance algorithms for large scale placement problem

Placement is one of the most important problems in electronic design automation (EDA). An inferior placement solution will not only affect the chip’s performance but might also make it nonmanufacturable by producing excessive wirelength, which is beyond available routing resources. Although placement has been extensively investigated for several decades, it is still a very challenging problem mainly due to that design scale has been dramatically increased by order of magnitudes and the increasing trend seems unstoppable. In modern design, chips commonly integrate millions of gates that require over tens of metal routing layers. Besides, new manufacturing techniques bring out new requests leading to that multi-objectives should be optimized simultaneously during placement. Our research provides high performance algorithms for placement problem. We propose (i) a high performance global placement core engine POLAR; (ii) an efficient routability-driven placer POLAR 2.0, which is an extension of POLAR to deal with routing congestion; (iii) an ultrafast global placer POLAR 3.0, which explore parallelism on POLAR and can make full use of multi-core system; (iv) some efficient triple patterning lithography (TPL) aware detailed placement algorithms

Parameterized complexity : permutation patterns, graph arrangements, and matroid parameters

The theory of parameterized complexity is an area of computer science focusing on refined analysis of hard algorithmic problems. In the thesis, we give two complexity lower bounds and define two novel parameters for matroids. The first lower bound is a kernelization lower bound for the Permutation Pattern Matching problem, which is concerned with finding a permutation pattern inside another input permutation. Our result states that unless a certain (widely believed) complexity hypothesis fails, it is impossible to construct a polynomial time algorithm taking an instance of the Permutation Pattern Matching problem and producing an equivalent instance of size bounded by a polynomial of the length of the pattern. Obtaining such lower bounds has been posed by Stephane Vialette as an open problem. We then prove a subexponential lower bound for the computational complexity of the Optimum Linear Arrangement problem. In our theorem, we assume a conjecture about the computational complexity of a variation of the Min Bisection problem. The two matroid parameters introduced in this work are called amalgam-width and branch-depth. Amalgam-width is a generalization of the branch-width parameter that allows for algorithmic applications even for matroids that are not finitely representable. We prove several results, including a theorem stating that deciding monadic second-order properties is fixed-parameter tractable for general matroids parameterized by amalgam-width. Branch-depth, the other newly introduced matroid parameter, is an analogue of graph tree-depth. We prove several statements relating graph tree-depth and matroid branch-depth. We also present an algorithm that efficiently approximates the value of the parameter on a general oracle-given matroid

Redistribution dynamique parallèle efficace de la charge pour les problèmes numériques de très grande taille

Cette thèse traite du problème de la redistribution dynamique parallèle efficace de la charge pour les problèmes numériques de très grande taille. Nous présentons tout d'abord un état de l'art des algorithmes permettant de résoudre les problèmes du partitionnement, du repartitionnement, du placement statique et du re-placement. Notre première contribution vise à étudier, dans un cadre séquentiel, les caractéristiques algorithmiques souhaitables pour les méthodes parallèles de repartitionnement. Nous y présentons notre contribution à la conception d'un schéma multi-niveaux k-aire pour le calcul sequentiel de repartitionnements. La partie la plus exigeante de cette adaptation concerne la phase d'expansion. L'une de nos contributions majeures a été de nous inspirer des méthodes d'influence afin d'adapter un algorithme de raffinement par diffusion au problème du repartitionnement.Notre deuxième contribution porte sur la mise en oeuvre de ces méthodes sur machines parallèles. L'adaptation du schéma multi-niveaux parallèle a nécessité une évolution des algorithmes et des structures de données mises en oeuvre pour le partitionnement. Ce travail est accompagné d'une analyse expérimentale, qui est rendue possible grâce à la mise en oeuvre des algorithmes considérés au sein de la bibliothèque Scotch.This thesis concerns efficient parallel dynamic load balancing for large scale numerical problems. First, we present a state of the art of the algorithms used to solve the partitioning, repartitioning, mapping and remapping problems. Our first contribution, in the context of sequential processing, is to define the desirable features that parallel repartitioning tools need to possess. We present our contribution to the conception of a k-way multilevel framework for sequential repartitioning. The most challenging part of this work regards the uncoarsening phase. One of our main contributions is the adaptation of influence methods to a global diffusion-based heuristic for the repartitioning problem. Our second contribution is the parallelization of these methods. The adaptation of the aforementioned algorithms required some modification of the algorithms and data structure used by existing parallel partitioning routines. This work is backed by a thorough experimental analysis, which is made possible thanks to the implementation of our algorithms into the Scotch library.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF