Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matching-based clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9 % for 100 runs and 3.0 to 20.6 % for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.

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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.

. This paper examines the effectiveness of load balancing strategies for ray tracing on large parallel computersystems and cluster computers. Popular static load balancing strategies are shown to be inadequate for rendering complex images with contemporary ray tracing algorithms, and for rendering NTSC resolution images on 128 or more computers. Strategies based on image tiling are shown to be ineffective except on very small numbers of computers. A dynamic load balancing strategy, based on a diffusion model, is applied to a parallel Monte Carlo rendering system. The diffusive strategy is shown to remedy the defects of the static strategies. A hybrid strategy that combines static and dynamic approaches produces nearly optimal performance on a variety of images and computer systems. The theoretical results should be relevant to other rendering and image processing applications. Keywords: load balancing, ray tracing, rendering, graphics, image processing, diffusion. 1. Introduction Hig...

This paper presents a cognitive vision system capable of autonomously learning protocols from perceptual observations of dynamic scenes. The work is motivated by the aim of creating a synthetic agent that can observe a scene containing interactions between unknown objects and agents, and learn models of these sufficient to act in accordance with the implicit protocols present in the scene. Discrete concepts (utterances and object properties), and temporal protocols involving these concepts, are learned in an unsupervised manner from continuous sensor input alone. Crucial to this learning process are methods for spatio-temporal attention applied to the audio and visual sensor data. These identify subsets of the sensor data relating to discrete concepts. Clustering within continuous feature spaces is used to learn object property and utterance models from processed sensor data, forming a symbolic description. The progol Inductive Logic Programming system is subsequently used to learn symbolic models of the temporal protocols presented in the presence of noise and over-representation in the symbolic data input to it. The models learned are used to drive a synthetic agent that can interact with the world in a semi-natural way. The system has been evaluated in the domain of table-top game playing and has been shown to be successful at learning protocol behaviours in such real-world audio-visual environments. Key words: cognitive vision, autonomous learning, unsupervised clustering, symbol grounding, inductive logic programming, spatio-temporal reasoning ∗ Corresponding author.

This paper describes a scalable photorealistic renderer that is designed to render scenes of arbitrary complexity on computer systems of arbitrary size. The rendering algorithm is a Monte Carlo method to compute approximate solutions of the rendering equation. The software implementation uses a diffusive load balancing method coupled with a message driven concurrent pipeline. Measured performance in rendering replicated models on up to 256 computers shows scaling efficiencies as high as 99 percent. Simple extensions will partition extremely large models across physically distributed memory as well as perform out-of-core calculations. 1 Introduction In recent years scalable parallel processors (SPPs) have become readily available to solve computationally intensive problems in science and engineering. Experience with these applications has shown that for certain classes of problems these SPPs routinely achieve speedups close to a factor of P using P

There are many important applications in computational fluid dynamics, circuit simulation and structural analysis that can be more accurately modeled using iterations on unstructured grids. In these problems, regular compiler analysis for Massively Parallel Processors (MPP) with distributed address space fails because communication can only be determined at run-time. However, in many of these applications the communication pattern repeats for every iteration. Therefore, equivalent optimizations to the regular case can be achieved with a combination of run-time support (RTS) and compiler analysis.

The top-down "quadratic placement" methodology is rooted in such works as [36] [9] [32] and is reputedly the basis of commercial and in-house VLSI placement tools. This methodology iterates between two basic steps: solving sparse systems of linear equations to achieve a continuous placement solution, and "legalization" of the placement by transportation or partitioning. Our work, which extends [5], studies implementation choices and underlying motivations for the quadratic placement methodology. We first recall some observations from [5], e.g., that (i) Krylov subspace engines for solving sparse linear systems This work was supported by a grant from Cadence Design Systems, Inc., and is an extension of work reported in Proc. ACM/IEEE Design Automation Conference, 1997 [5]. Author to whom correspondence should be addressed: Prof. Andrew B. Kahng, UCLA Computer Science Department, 3713 Boelter Hall, Los Angeles, CA 90095-1596 USA. abk@cs.ucla.edu, http://vlsicad.cs.ucla.edu/.

Several graph visualization tools exist. However, they are not able to handle large graphs, and/or they do not allow interaction. We are interested on large graphs, with hundreds of thousands of nodes. Such graphs bring two challenges: the first one is that any straightforward interactive manipulation will be prohibitively slow. The second one is sensory overload: even if we could plot and replot the graph quickly, the user would be overwhelmed with the vast volume of information because the screen would be too cluttered as nodes and edges overlap each other. Our GMine system addresses both these issues, by using summarization and multi-resolution. GMine offers multi-resolution graph exploration by partitioning a given graph into a hierarchy of communities-within-communities and storing it into a novel R-tree-like structure which we name G-Tree. GMine offers summarization by implementing an innovative subgraph extraction algorithm and then visualizing its output. 1.

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