integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations....
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integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/epsilon) . poly(vertical bar I vertical bar). Previously, only constant factor approximations of 5/3 and 4/3 + epsilon, respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.
Mobile edge computing system provides cloud computing capabilities at the edge of wireless mobile networks, ensuring low latency, highly efficient computing, and improved user experience. At the same time, computation...
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Mobile edge computing system provides cloud computing capabilities at the edge of wireless mobile networks, ensuring low latency, highly efficient computing, and improved user experience. At the same time, computationally intensive components are offloaded from mobile devices to edge servers and distributed among the servers. Due to the special constraints (mobile devices' battery capacities, limited computing resources of one single edge server, inevitable edge server failure, etc.), there emerges a following problem. 1) How to guarantee the reliability of the offloaded computing? This problem brings in the following two other problems. 2) How to find the appropriate offloading point in the mobile program such that the computing tasks offloaded to cloud can be maximized, while the transmission energy consumption is minimized? 3) What is the achievable minimum latency tasks allocation strategy among multiple users' mobile devices and multiple edge servers? In this paper, we try to address the aforementioned problems. First, for the appropriate offloading point problem, we consider the offloading valuable basic constraint and propose a task merging strategy based on mobile program component call graphs to minimize the computational complexity of the program partition. Second, we formulate the second problem as a combinatorial optimization problem and transform it into ann-fold integer programming problem by mapping the remaining computing resources to a virtual component. Third, we design a reliable shadow component scheme between multilevel severs for the reliability problem. Finally, we develop a fast algorithm for the mix problem and analyze its performance and conduct experiments to prove the accuracy of our theoretical results.
We introduce a general problem about bribery in voting systems. In the R-MULTI-BRIBERY problem, the goal is to bribe a set of voters at minimum cost such that a desired candidate wins the manipulated election under th...
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ISBN:
(纸本)9783959770286
We introduce a general problem about bribery in voting systems. In the R-MULTI-BRIBERY problem, the goal is to bribe a set of voters at minimum cost such that a desired candidate wins the manipulated election under the voting rule R. Voters assign prices for withdrawing their vote, for swapping the positions of two consecutive candidates in their preference order, and for perturbing their approval count for a candidate. As our main result, we show that R-MULTI-BRIBERY is fixed-parameter tractable parameterized by the number of candidates for many natural voting rules R, including Kemeny rule, all scoring protocols, maximin rule, Bucklin rule, fallback rule, SP-AV, and any Cl rule. In particular, our result resolves the parameterized of R-SwAP BRIBERY for all those voting rules, thereby solving a long-standing open problem and "Challenge #2" of the 9 Challenges in computational social choice by Bredereck et al. Further, our algorithm runs in single-exponential time for arbitrary cost;it thus improves the earlier double-exponential time algorithm by Dorn and Schlotter that is restricted to the unit-cost case for all scoring protocols, the maximin rule, and Bucklin rule.
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