In single machine scheduling with release times and job delivery, jobs are processed on single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jo...
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In single machine scheduling with release times and job delivery, jobs are processed on single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs in a shipment. The delivery completion time of a job is defined as the time in which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. We provide an approximation algorithm for this problem which is better than that given in the literature, improving the performance ratio from 5/3 to 3/2. (C) 2010 Elsevier B.V. All rights reserved.
A new efficient two-dimensional warping algorithm is presented, in which sub-optimal warping is attained by iterating DP-based local optimization of warp on partially overlapping subplane sequence. From an experimenta...
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A new efficient two-dimensional warping algorithm is presented, in which sub-optimal warping is attained by iterating DP-based local optimization of warp on partially overlapping subplane sequence. From an experimental comparison with a conventional approximation algorithm based on beam search DP, relative superiority of the proposed algorithm is established.
The Capacitated Multicast Tree Routing Problem is considered, in which only a limited number of destination nodes are allowed to receive data in one routing tree and multiple routing trees are needed to send data from...
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ISBN:
(纸本)9783540850960
The Capacitated Multicast Tree Routing Problem is considered, in which only a limited number of destination nodes are allowed to receive data in one routing tree and multiple routing trees are needed to send data from the source node to all destination nodes. The goal is to minimize the total cost of these routing trees. An improved approximation algorithm is presented, which has a worst case performance ratio of 8/5 + 5/4 rho. Here rho denotes the best approximation ratio for the Steiner Minimum Tree problem, and it is about 1.55 at the writing of the paper. This improves upon the previous best having a performance ratio of 2+rho.
Scheduling task graphs with communication delay is a widely studied NP-hard problem. Many heuristics have been proposed, but there is no constant approximation algorithm for this classic model. In this paper, we focus...
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ISBN:
(纸本)9798350337662
Scheduling task graphs with communication delay is a widely studied NP-hard problem. Many heuristics have been proposed, but there is no constant approximation algorithm for this classic model. In this paper, we focus on the scheduling of the important class of fork-join task graphs (describing many types of common computations) on homogeneous processors. For this sub-case, we propose a guaranteed algorithm with a (1+ m m-1)approximation factor, where m is the number of processors. The algorithm is not only the first constant approximation for an important sub-domain of the classic scheduling problem, it is also a practical algorithm that can obtain shorter makespans than known heuristics. To demonstrate this, we propose adaptations of known scheduling heuristic for the specific fork-join structure. In an extensive evaluation, we then implemented these algorithms and scheduled many fork-join graphs with up to thousands of tasks and various computation time distributions on up to hundreds of processors. Comparing the obtained results demonstrates the competitive nature of the proposed approximation algorithm.
The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the t...
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The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ??>?0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (k_ u , k _l ), our algorithm constructs a vertex cover of size (k~* _u , k~* _l ), satisfying max {k~ *_u /k _u , k ~*_ l /k_ l }?≤?1?+??. Electronic supplementary material The online version of this article (doi: 10.1007/s11390-008-9180-5) contains supplementary material, which is available to authorized users.
This paper is aimed to present the solution to vertex cover problem by means of an approximation solution. As it is NP complete problem, we can have an approximate time algorithm to solve the vertex cover problem. We ...
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ISBN:
(纸本)9788132221265;9788132221258
This paper is aimed to present the solution to vertex cover problem by means of an approximation solution. As it is NP complete problem, we can have an approximate time algorithm to solve the vertex cover problem. We will modify the algorithm to have an algorithm which can be solved in polynomial time and which will give near to optimum solution. It is a simple algorithm which will be based on articulation point. Articulation point can be found using the Depth First Search algorithm.
In this paper, we consider the dynamic k-level facility location problem, which is a generalization of the uncapacitated k-level facility location problem when considering time factor. We present a combinatorial prima...
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ISBN:
(纸本)9783030271954;9783030271947
In this paper, we consider the dynamic k-level facility location problem, which is a generalization of the uncapacitated k-level facility location problem when considering time factor. We present a combinatorial primal-dual approximation algorithm for the problem which finds a solution within 6 times the optimum. This approximation ratio under a dynamic setting coincides with that of the simple dual ascent 6-approximation algorithm for the (static) multilevel facility location problem (Bumb, 2001) with a weak triangle inequality property.
In single machine scheduling with release times and job delivery, jobs are processed on single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jo...
详细信息
In single machine scheduling with release times and job delivery, jobs are processed on single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs in a shipment. The delivery completion time of a job is defined as the time in which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. We provide an approximation algorithm for this problem which is better than that given in the literature, improving the performance ratio from 5/3 to 3/2. (C) 2010 Elsevier B.V. All rights reserved.
(1) We consider the following classical resource constrained scheduling problem. Given m identical processors, s resources R-1,..., R-s with upper bounds b(1),..., b(s), n independent jobs T-1,...,T-n of unit length, ...
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ISBN:
(纸本)3540631380
(1) We consider the following classical resource constrained scheduling problem. Given m identical processors, s resources R-1,..., R-s with upper bounds b(1),..., b(s), n independent jobs T-1,...,T-n of unit length, where each job requires one processor and an amount R-i(j) is an element of {0, 1} of resource R-i, i = 1,..., s, the optimization problem is to schedule the jobs at discrete times in (1,..., n) subject to the processor and resource constraints so that the latest scheduling time is minimum. Note that multidimensional bin packing is a special case of this problem. We give for every fixed alpha > 1 the first parallel 2 alpha-factor approximation algorithm and show that there cannot exist a polynomial-time approximation algorithm achieving an approximation factor better than 4/3, unless P = NP.
With new learning technologies springing up, gaming also plays a vital role in creating learning experiences. Studies show that games play an active role in defining active and creative learning activities. For effect...
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ISBN:
(纸本)9781728152868
With new learning technologies springing up, gaming also plays a vital role in creating learning experiences. Studies show that games play an active role in defining active and creative learning activities. For effective learning through game based activities, games need to be well defined, interactive and challenging. Gamification can be applied in the context of learning using Atificial Intelligence. It is understood that game development is one of the use cases for AI. An attempt had been made to gamily learning using a supervised learning based approximation technique. The case study is done with TRON game using an alternate Voronoi heuristics, employing supervised learning. The algorithm has been tested for different game scenarios and the proposed game hot was tested for accuracy of moves, winning percentage and response time.
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