Ali Pinar

On Identifying Strongly Connected Components in Parallel

The standard serial algorithm for strongly connected components is based on depth first search, which is difficult to parallelize. We describe a divide-and-conquer algorithm for this problem which has significantly greater potential for parallelization. For a graph with n vertices in which degrees are bounded by a constant, we sho w the expected serial running time of our algorithm to be O(n log n).

Partitioning for complex objectives

Graph partitioning is an important tool for dividing work amongst processors of a parallel machine, but it is unsuitable for some important applications. Specifically, graph partitioning requires the work per processor to be a simple sum of vertex weights. For many applications, this assumption is not true — the work (or memory) is a complex function of the partition. In this paper we describe a general framework for addressing such partitioning problems and investigate its utility on two applications — partitioning so that overlapped subdomains are balanced and partitioning to minimize the sum of computation plus communication time.

Power invariant vector sequence compaction

Simulation-based power estimation is commonly used for its high accuracy, despite excessive computation times. Techniques have been proposed to speed it up by transforming a given sequence into a shorter one while preserving the power consumption characteristics of the original sequence. This work proposes a novel method to compact a given input vector sequence to improve on the existing techniques. We propose a graph model to transform the problem to the problem of finding a heaviest weighted trail in a directed graph. We also propose a heuristic based on min-cost flow algorithms, using the graph model. Furthermore, we show that generating multiple input sequences yields better solutions in terms of both accuracy and simulation time. Experiments showed that significant reduction in simulation times can be achieved with extremely accurate results. Experiments also showed that the generation of multiple sequences improved the results further both in terms of accuracy and simulation time.

Interprocessor communication with memory constraints

Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. We propose a model for optimizing the exchange of messages under such circumstances which we call the minimum phase remapping problem. We first show that the problem is NP-Complete, and then analyze several methodologies for addressing it. First, we show how the problem can be phrased as an instance of multi-commodity flow. Next, we study a continuous approximation to the problem. We show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. Finally, we devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases.