Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Computing Mobile Agent Routes with Node-Wise Constraints in Distributed Communication Systems

10th Mexican International Conference on Artificial Intelligence, MICAI 2011, Puebla, 26 November-4 December 2011A basic problem in the quality-of-service (QoS) analysis of multiagent distributed systems is to find optimal routes for the mobile agents that incrementally fuse the data as they visit hosts in the distributed system. The system is modeled as a directed acyclic graph in which the nodes represent hosts and the edges represent links between them. Each edge is assigned a cost (or benefit) and weights that represent link delay, reliability, or other QoS parameters. The agent scheduling problem is viewed as a constrained routing problem in which a maximum-benefit (or minimum-cost) route connecting the source and the destination subject to QoS constraints is to be found. We study approximation algorithms called 'fully polynomial time approximation schemes' (FPTAS) for solving the problem. We suggest an accelerating technique that improves known FPTAS, e.g., Hassin's (1992); Camponogara & Shima's (2010); and Elalouf et al. (2011) algorithms, and present new FPTASs.Department of Logistics and Maritime Studie

Efficient Routing of Mobile Agents for Agent-Based Integrated Enterprise Management: A General Acceleration Technique

7th International Workshop on Enterprise and Organizational Modeling and Simulation, EOMAS 2011, in Conjunction with CAiSE 2011, London, 20-21 June 2011Modern manufacturing enterprises are steadily moving towards open architectures wherein manufacturing activities are integrated with the activities of suppliers, customers, and partners within complex supply chains. Agent-based technology provides a natural way to design and implement such integration. We model the supply chain as a directed graph in which the vertices represent computers or individual agents and edges represent links. Thus the problem of enhancing the efficiency of mobile agents reduces to the problem of finding resource-constrained extremal paths in the graph. We study ε-approximation algorithms for solving the considered problems. We suggest a general three-stage technique, which follows and extends an earlier computational scheme in the literature for the constrained path problems (CPP). The new technique essentially improves on several earlier algorithms and also provides new aproach for contructing FPTAS for the CPP.Department of Logistics and Maritime Studie

Approximation schemes for a class of subset selection problems

In paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show up in many places in the literature. For every such special case, a particular rounding trick has been implemented in a slightly different way, with slightly different arguments, and with slightly different worst case estimations. Usually, the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument. Our easily applied result unifies many of these results, and sometimes it even leads to a simpler proof. We demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems. As a special case, we derive the existence of an FPTAS for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine. The approximability status of this problem has been open for some time