Myoung-Ju Park

A pseudo-polynomial heuristic for path-constrained discrete-time Markovian-target search

We propose a new heuristic for the single-searcher path-constrained discrete-time Markovian-target search. The algorithm minimizes an approximate, instead of exact, nondetection probability computed from the conditional probability that reflects the search history over the time windows of a fixed length, l. Having a pseudo-polynomial complexity, it can solve, in reasonable time, the instances an order of magnitude larger than those solved in the previous studies. By an asymptotic analysis relying on the fast-mixing Markov chain, we show that the relative error of the approximation exponentially diminishes as l increases and the experimental results confirm the analysis. The experiment also reveals a correlation very close to 1 between the approximate and exact nondetection probability of a search path. This means that the heuristic produces near-optimal search paths.

Optimal search-relocation trade-off in Markovian-target searching

In this study, a standard moving-target search model was extended with a multiple-search-speed option, whereby a trade-off is enabled between the increased detection chances owing to the searchers better location and the increased uncertainty of the targets location resulting from the diminished search performance incurred in the relocation. This enhances the detection probability of the output search path and, thereby, the models practicality. However, the scalability of the solution method is essential to its implementation, as the basic model is already NP-hard. We developed an efficient heuristic by combining the idea of approximate nondetection probability minimization and a hybridized shortest-path heuristic that exploits the fast-mixing property of the Markov chain. According to the results of an intensive experiment, the heuristic achieves a near-optimal trade-off within a very reasonable computation time.

Dynamic task assignment and resource management in cloud services by using bargaining solution

Cloud computing provides infrastructure, platform and software as services to customers. For the purpose of providing reliable and truthful service, a fair and elastic resource allocation strategy is essential from the standpoint of service customers. In this paper, we propose a game theoretic mechanism for dynamic cloud service management, including task assignment and resource allocation to provide reliable and truthful cloud services. A user utility function is first devised considering the dynamic characteristics of cloud computing. The elementary stepwise system is then applied to efficiently assign tasks to cloud servers. A resource allocation mechanism based on bargaining game solution is also adopted for fair resource allocation in terms of quality of service of requested tasks. Through numerical experiments, it is shown that the proposed mechanism guarantees better system performance than several existing methods. The experimental results show that the mechanism completes the requested tasks earlier with relatively higher utility while providing a significant level of fairness compared with existing ones. The proposed mechanism is expected to support cloud service providers in elastically managing their limited resources in a cloud computing environment in terms of quality of service. Copyright

A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs

We consider a continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs. If a milestone is tardy, a penalty cost may be imposed. The processing times of jobs can be compressed by additional resources or activities that incur compression costs. The objective is to minimize the total penalty cost plus the total compression cost. We show that the problem is NP-hard, even if the compression cost is described as a concave function, and we present a pseudo-polynomial time algorithm for that case. Furthermore, we show that the problem is polynomially solvable if the compression cost function is convex.

Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications

It has been observed that the Handelman’s certificate of positivity of a polynomial over a compact polyhedron offers a hierarchical relaxation scheme for polynomial programs. The Handelman hierarchy seems particularly suitable for a class of combinatorial optimizations that are formulated as a zero-diagonal quadratic program over a hypercube. In this paper, we present an error analysis of Handelman hierarchy applied to the special class of polynomial programs and its implications in the computation of the combinatorial optimization problems.

Rank of Handelman hierarchy for Max-Cut

Abstract We consider a hierarchical relaxation, called Handelman hierarchy, for a class of polynomial optimization problems. We prove that the rank of Handelman hierarchy, if applied to a standard quadratic formulation of Max-Cut, is exactly the same as the number of nodes of the underlying graph. Also we give an error bound for Handelman hierarchy, in terms of its level, applied to the Max-Cut formulation.

Approximation of the k-batch consolidation problem

We consider a problem of minimizing the number of batches of a fixed capacity processing the orders of various sizes on a finite set of items. This batch consolidation problem is motivated by the production system typical in raw material industries in which multiple items can be processed in the same batch if they share sufficiently close production parameters. If the number of items processed in a batch is restricted to being up to some fixed integer k, the problem is referred to as the k-batch consolidation problem. We will show that the k-batch consolidation problem admits an approximation whose factor is twice that of the k-set cover problem. In particular, this implies an upper bound on the approximation factor, 2Hk-1, where Hk=1+½+...+1/k.

Two-agent parallel machine scheduling with a restricted number of overlapped reserved tasks

We consider a two-agent scheduling problem on parallel machines such that each task of agent 2 has a given time window. Furthermore, we introduce a resource constraint under which the number of simultaneously processed tasks of agent 2 is restricted, although some machines are available. The objective is to minimize the total completion time for agent 1 while the total weight of the processed tasks for agent 2 is at or above a given threshold. Because the problem is known to be strongly NP-hard, we focus on the case with unit processing time. We analyze the computational complexity for its special cases, which have some restrictions on four parameters: the weight and the duration of agent 2, the number of machines, and the maximum number of simultaneously processed tasks of agent 2.

An Ordered Flow Shop with Two Agents

In this paper, we consider a two-agent scheduling problem in an m-machine ordered flow shop where each agent is responsible for his own set of jobs and wishes to minimize the makespan. Since the problem is NP-hard, we develop a pseudo-polynomial time approach for the case with a fixed number of machines and investigate the conditions that make the problem polynomially solvable. Finally, we consider a three-machine problem with a special processing time structure, and demonstrate its polynomiality.

A Batch Scheduling Problem with Two Agents

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.