Independent task assignment for heterogeneous systems

Abstract

We study the problem of assigning nonuniform tasks onto heterogeneous systems. We investigate two distinct problems in this context. The first problem is the one-dimensional partitioning of nonuniform workload arrays with optimal load balancing. The second problem is the assignment of nonuniform independent tasks onto heterogeneous systems. For one-dimensional partitioning of nonuniform workload arrays, we investigate two cases: chain-on-chain partitioning (CCP), where the order of the processors is specified, and chain partitioning (CP), where processor permutation is allowed. We present polynomial time algorithms to solve the CCP problem optimally, while we prove that the CP problem is NP complete. Our empirical studies show that our proposed exact algorithms for the CCP problem produce substantially better results than the state-of-the-art heuristics while the solution times remain comparable. For the independent task assignment problem, we investigate improving the performance of the well-known and widely used constructive heuristics MinMin, MaxMin and Sufferage. All three heuristics are known to run in O(KN2 ) time in assigning N tasks to K processors. In this thesis, we present our work on an algorithmic improvement that asymptotically decreases the running time complexity of MinMin to O(KN log N) without affecting its solution quality. Furthermore, we combine the newly proposed MinMin algorithm with MaxMin as well as Sufferage, obtaining two hybrid algorithms. The motivation behind the former hybrid algorithm is to address the drawback of MaxMin in solving problem instances with highly skewed cost distributions while also improving the running time performance of MaxMin. The latter hybrid algorithm improves the running time performance of Sufferage without degrading its solution quality. The proposed algorithms are easy to implement and we illustrate them through detailed pseudocodes. The experimental results over a large number of real-life datasets show that the proposed fast MinMin algorithm and the proposed hybrid algorithms perform significantly better than their traditional counterparts as well as more recent state-of-the-art assignment heuristics. For the large datasets used in the experiments, MinMin, MaxMin, and Sufferage, as well as recent state-of-the-art heuristics, require days, weeks, or even months to produce a solution, whereas all of the proposed algorithms produce solutions within only two or three minutes. For the independent task assignment problem, we also investigate adopting the multi-level framework which was successfully utilized in several applications including graph and hypergraph partitioning. For the coarsening phase of the multi-level framework, we present an efficient matching algorithm which runs in O(KN) time in most cases. For the uncoarsening phase, we present two refinement algorithms: an efficient O(KN)-time move-based refinement and an efficient O(K2N log N)-time swap-based refinement. Our results indicate that multi-level approach improves the quality of task assignments, while also improving the running time performance, especially for large datasets. As a realistic distributed application of the independent task assignment problem, we introduce the site-to-crawler assignment problem, where a large number of geographically distributed web servers are crawled by a multi-site distributed crawling system and the objective is to minimize the duration of the crawl. We show that this problem can be modeled as an independent task assignment problem. As a solution to the problem, we evaluate a large number of state-of-the-art task assignment heuristics selected from the literature as well as the improved versions and the newly developed multi-level task assignment algorithm. We compare the performance of different approaches through simulations on very large, real-life web datasets. Our results indicate that multi-site web crawling efficiency can be considerably improved using the independent task assignment approach, when compared to relatively easy-to-implement, yet naive baselines.