We are given a set of m identical parallel machines and a set of n jobs in large computing systems, where each job J(j) consists of a bag of bj identical tasks with a processing time p(j), and has a rejection penalty ...
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We are given a set of m identical parallel machines and a set of n jobs in large computing systems, where each job J(j) consists of a bag of bj identical tasks with a processing time p(j), and has a rejection penalty wj. Job J(j )is either accepted in which case all the b(j) tasks must be processed by one of the machines, or rejected which incurs a rejection penalty w(j). The problem of bag-of-tasks scheduling with rejection is to find a feasible schedule, so as to minimize the makespan plus the total rejection penalty of all rejected jobs. In this paper, we present a polynomial time approximation scheme.
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is ...
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Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient analog of the Steiner tree problem arising, for example, in telecommunications applications. We study a more generalmixed-connectivity formulation, also employed in telecommunications optimization. Given a number (or requirement) r(v) is an element of{0, 1, 2} for each vertex v in the graph, find a minimum-cost subgraph in which there are min{r(u), r(v)} edge-disjoint u-to-v paths for every pair u, v of vertices. We address the problem in planar graphs, considering a popular relaxation in which the solution is allowed to use multiple copies of the input-graph edges (paying separately for each copy). The problem is max SNP-hard in general graphs and strongly NP-hard in planar graphs. We give the first polynomial-timeapproximationscheme in planar graphs. The running time is O(n log n). Under the additional restriction that the requirements are only non-zero for vertices on the boundary of a single face of a planar graph, we give a polynomial-time algorithm to find the optimal solution.
In the context of mobile edge computing (MEC), the delay-sensitive tasks can achieve real-time data processing and analysis by offloading to the MEC servers. The objective is maximizing social welfare in an auction- b...
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In the context of mobile edge computing (MEC), the delay-sensitive tasks can achieve real-time data processing and analysis by offloading to the MEC servers. The objective is maximizing social welfare in an auction- based model. However, the distances between mobile devices and access points lead to differences in energy consumption. Unfortunately, existing works have not considered both maximizing social welfare and minimizing energy consumption. Motivated by this, we address the problem of joint resource allocation and task offloading in MEC, with heterogeneous MEC servers providing multiple types of resources for mobile devices (MDs) to perform tasks remotely. We split the problem into two sub-problems: winner determination and offloading decision. The first sub-problem determines winners granted the ability to offload tasks to maximize social welfare. The second sub-problem determines how to offload tasks among the MEC servers to minimize energy consumption. In the winner determination problem, we propose a truthful algorithm that drives the system into equilibrium. We then show the approximate ratios for single and multiple MEC servers. In the offloading decision problem, we propose an approximation algorithm. We then show it is a polynomial- timeapproximationscheme for a single MEC server. Experiment results show that our proposed mechanism finds high-quality solutions in changing mobile environments.
We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the long...
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We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme （PTAS） and a fully polynomial time approximation scheme （FPTAS） for this problem.
The prediction of RNA structure with pseudoknots is NP-hard problem. According to minimum free energy models and computational methods, we investigate the RNA pseudoknotted structures and their characteristics. The pa...
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The prediction of RNA structure with pseudoknots is NP-hard problem. According to minimum free energy models and computational methods, we investigate the RNA pseudoknotted structures and their characteristics. The paper presents an efficient algorithm for predicting RNA structures with pseudoknots, and the algorithm runs in O(n(3)) time and O(n(2)) space. The experimental tests in Rfam 10.1 and PseudoBase indicate that the algorithm is more effective and precise, and the algorithm can predict arbitrary pseudoknots. And through our research, we can draw that there exists an 1 + epsilon (epsilon > 0) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximationscheme in RNA pseudoknotted structures.
Scheduling on Unrelated Machines is a classical optimization problem where n jobs have to be distributed to m machines. Each of the jobs j is an element of {1,...,n} has on machine i is an element of{ 1,...,m} a proce...
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Scheduling on Unrelated Machines is a classical optimization problem where n jobs have to be distributed to m machines. Each of the jobs j is an element of {1,...,n} has on machine i is an element of{ 1,...,m} a processing time p(ij) >= 0 . The goal is to minimize the makespan, i.e. the maximum completion time of the longest-running machine. Unless P=NP , this problem does not allow for a polynomial-timeapproximation algorithm with a ratio better than 32 . A natural scenario is however that many machines are of the same type, like a CPU and GPU cluster: for each of the K machine types, the machines i not equal i' of the same type k satisfy p(ij) = p(i'j) for all jobs j. For the case where the number K of machine types is constant, this paper presents an approximationscheme, i.e. an algorithm of approximation ratio 1+ epsilon for epsilon > 0 , with an improved running time only single exponential in 1/epsilon .
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