Exact algorithms for a task assignment problem

We consider the following task assignment problem. Communicating tasks are to be assigned to heterogeneous processors interconnected with a heterogeneous network. The objective is to minimize the total sum of the execution and communication costs. The problem is NP-hard. We present an exact algorithm based on the well-known A* search. We report simulation results over a wide range of parameters where the largest solved instance contains about three hundred tasks to be assigned to eight processors. © World Scientific Publishing Company

Independent task assignment for heterogeneous systems

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent Univ., 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 136-150.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.Tabak, E KartalPh.D

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

Optimal Inference in Crowdsourced Classification via Belief Propagation

Crowdsourcing systems are popular for solving large-scale labelling tasks with low-paid workers. We study the problem of recovering the true labels from the possibly erroneous crowdsourced labels under the popular Dawid-Skene model. To address this inference problem, several algorithms have recently been proposed, but the best known guarantee is still significantly larger than the fundamental limit. We close this gap by introducing a tighter lower bound on the fundamental limit and proving that Belief Propagation (BP) exactly matches this lower bound. The guaranteed optimality of BP is the strongest in the sense that it is information-theoretically impossible for any other algorithm to correctly label a larger fraction of the tasks. Experimental results suggest that BP is close to optimal for all regimes considered and improves upon competing state-of-the-art algorithms.Comment: This article is partially based on preliminary results published in the proceeding of the 33rd International Conference on Machine Learning (ICML 2016

Hierarchies of Inefficient Kernelizability

The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However, there are also some issues that are not addressed by this framework, including the existence of Turing kernels such as the "kernelization" of Leaf Out Branching(k) into a disjunction over n instances of size poly(k). Observing that Turing kernels are preserved by polynomial parametric transformations, we define a kernelization hardness hierarchy, akin to the M- and W-hierarchy of ordinary parameterized complexity, by the PPT-closure of problems that seem likely to be fundamentally hard for efficient Turing kernelization. We find that several previously considered problems are complete for our fundamental hardness class, including Min Ones d-SAT(k), Binary NDTM Halting(k), Connected Vertex Cover(k), and Clique(k log n), the clique problem parameterized by k log n

MC-Fluid: Fluid Model-Based Mixed-Criticality Scheduling on Multiprocessors

A mixed-criticality system consists of multiple components with different criticalities. While mixed-criticality scheduling has been extensively studied for the uniprocessor case, the problem of efficient scheduling for the multiprocessor case has largely remained open. We design a fluid model-based multiprocessor mixed-criticality scheduling algorithm, called MC-Fluid in which each task is executed in proportion to its criticality-dependent rate. We propose an exact schedulability condition for MC-Fluid and an optimal assignment algorithm for criticality-dependent execution rates with polynomial-time complexity. Since MC-Fluid cannot be implemented directly on real hardware platforms, we propose another scheduling algorithm, called MC-DP-Fair, which can be implemented while preserving the same schedulability properties as MC-Fluid. We show that MC-Fluid has a speedup factor of (1 + √ 5) /2 (~ 1.618), which is best known in multiprocessor MC scheduling, and simulation results show that MC-DP-Fair outperforms all existing algorithms