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Tight bounds for online classconstrained packing
 Lecture Notes in Computer Science
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An Experimental Study of kSplittable Scheduling for DNSBased Traffic Allocation
 EUROPAR 2003 PARALLEL PROCESSING, 9TH INTERNATIONAL EUROPAR CONFERENCE
, 2003
"... The Internet domain name system (DNS) uses rotation of address lists to perform load distribution among replicated servers. We model this kind of load balancing mechanism in form of a set of request streams with different rates that should be mapped to a set of servers. Rotating a list of length k ..."
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The Internet domain name system (DNS) uses rotation of address lists to perform load distribution among replicated servers. We model this kind of load balancing mechanism in form of a set of request streams with different rates that should be mapped to a set of servers. Rotating a list of length k corresponds to breaking streams into k equally sized pieces. We compare this and other strategies of how to break the streams into a bounded number of pieces and how to map these pieces to the servers. One of the strategies that we study computes an optimal ksplittable allocation using a scheduling algorithm that breaks streams into at most k ≥ 2 pieces of possibly different size and maps these pieces to the servers in such a way that the maximum load over all servers is minimized. Our experimental study is done using the network simulator SSFNet. We study the average and maximum delay experienced by HTTP requests for various traffic allocation policies and traffic patterns. Our simulations show that splitting data streams can reduce the maximum as well as the average latency of HTTP requests significantly. This improvement can be observed even if streams are simply broken into k equally sized pieces that are mapped randomly to the servers. Using allocations computed by machine scheduling algorithms, we observe further significant improvements.
Online Scheduling of Splittable Tasks
 IN PEERTOPEER NETWORKS, PROCEEDINGS OF SWAT, LNCS
, 2004
"... We consider online scheduling of splittable tasks on parallel machines. In our model, each task can be split into a limited number of parts, that can then be scheduled independently. We consider both the case where the machines are identical and the case where some subset of the machines have a (fix ..."
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We consider online scheduling of splittable tasks on parallel machines. In our model, each task can be split into a limited number of parts, that can then be scheduled independently. We consider both the case where the machines are identical and the case where some subset of the machines have a (fixed) higher speed than the others. We design a class of algorithms which allows us to give tight bounds for a large class of cases where tasks may be split into relatively many parts. For identical machines we also improve upon the natural greedy algorithm in other classes of cases.
A Note on Dual Approximation Algorithms for Class Constrained Bin Packing Problems
"... In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of di ..."
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In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size d. In a shelf bin packing problem, we have to obtain a shelf packing such that the total size of items and shelf divisors in any bin is at most 1. A dual approximation scheme must obtain a shelf packing of all items into N bins, such that, the total size of all items and shelf divisors packed in any bin is at most 1+ε for a given ε > 0 and N is the number of bins used in an optimum shelf bin packing problem. Shelf divisors are used to avoid contact between items of different classes and can hold a set of items until a maximum given weight. We also present a dual approximation scheme for the class constrained bin packing problem. In this problem, there is no use of shelf divisors, but each bin uses at most C different classes.
On the Existence of Pure Strategy Nash Equilibria in Integer–Splittable Weighted Congestion Games
"... Abstract. We study the existence of pure strategy Nash equilibria (PSNE) in integer–splittable weighted congestion games (ISWCGs), where agents can strategically assign different amounts of demand to different resources, but must distribute this demand in fixedsize parts. Such scenarios arise in a ..."
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Abstract. We study the existence of pure strategy Nash equilibria (PSNE) in integer–splittable weighted congestion games (ISWCGs), where agents can strategically assign different amounts of demand to different resources, but must distribute this demand in fixedsize parts. Such scenarios arise in a wide range of application domains, including job scheduling and network routing, where agents have to allocate multiple tasks and can assign a number of tasks to a particular selected resource. Specifically, in an ISWCG, an agent has a certain total demand (aka weight) that it needs to satisfy, and can do so by requesting one or more integer units of each resource from an element of a given collection of feasible subsets.1 Each resource is associated with a unit–cost function of its level of congestion; as such, the cost to an agent for using a particular resource is the product of the resource unit–cost and the number of units the agent requests. While general ISWCGs do not admit PSNE (Rosenthal, 1973b), the restricted subclass of these games with linear unit–cost functions has been shown to possess a potential function (Meyers, 2006), and hence, PSNE. However, the linearity of costs may not be necessary for the existence of equilibria in pure strategies. Thus, in this paper we prove that PSNE always exist for a larger class of convex and monotonically increasing unit–costs. On the other hand, our result is accompanied by a limiting asumption on the structure of agents ’ strategy sets: specifically, each agent is associated with its set of accessible resources, and can distribute its demand across any subset of these resources.
Online Scheduling of Splittable Tasks in PeerToPeer Networks
, 2004
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.
Online Task Allocation in ClientServer Large Scale Heterogeneous Platforms
"... In this paper, we consider the problem of the online allocation of a very large number of identical tasks on a masterslave platform. Initially, several masters hold or generate tasks that are transfered and processed by slave nodes. The goal is to maximize the overall throughput achieved using thi ..."
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In this paper, we consider the problem of the online allocation of a very large number of identical tasks on a masterslave platform. Initially, several masters hold or generate tasks that are transfered and processed by slave nodes. The goal is to maximize the overall throughput achieved using this platform, i.e., the (fractional) number of tasks that can be processed within one time unit. We model the communications using the socalled bounded degree multiport model, in which several communications can be handled by a master node simultaneously, provided that bandwidths limitation are not exceeded and that a given server is not involved in more simultaneous communications than its maximal degree. Under this model, it has been proved in [1] that maximizing the throughput (MTBD problem) is NPComplete in the strong sense but that a small additive resource augmentation (of 1) on the servers degrees is enough to find in polynomial time a solution that achieves at least the optimal throughput. In this paper, we consider the reasonable setting where the set of slave processors is not known in advance but rather join and leave the system at any time, i.e., the online version of MTBD. We prove that no fully online algorithm (where only one change is allowed for each event) can achieve a constant approximation ratio, whatever the resource augmentation on servers degrees. Then, we prove that it is possible to maintain the optimal solution at the cost of at most four changes per server each time a new node joins or leaves the system. At last, we propose several other greedy heuristics to solve the online problem and we compare the performance (in terms of throughput) and the cost (in terms of disconnections and reconnections) of proposed algorithms through a set of extensive simulation results.
The power of preemption . . .
, 2012
"... Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worstcase ratio between the makespan of an optimal nonpreemptive and that of an ..."
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Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worstcase ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitter [Lin, J.H., J. S. Vitter. 1992. approximations with minimum packing constraint violation. Proc. 24th Annual ACM Sympos. Theory of Comput. (STOC), ACM, New York, 771–782] two decades ago. In the second part of the paper, we consider the more general setting in which orders, consisting of several jobs, have to be processed on unrelated parallel machines so as to minimize the sum of weighted completion times of the orders. We obtain the first constant factor approximation algorithms for the preemptive and nonpreemptive cases, improving and extending a recent result by Leung et al. [Leung, J., H. Li, M. Pinedo, J. Zhang. 2007. Minimizing total weighted completion time when scheduling orders in a flexible environment with uniform machines. Inform. Processing Lett. 103 119–129]. Finally, we study this problem in a parallel machine environment, obtaining a polynomialtime approximation scheme for several special cases.
Optimization by Ant Colony hybrid Local Search for online Class Constrained Bin Packing problem TsaiDuan Lin1,2,a, ChiunChieh Hsu1,b and LiFu Hsu1,2,c
"... Abstract. The online Class Constrained Bin Packing problem (CCBP) is one of variant version of the Bin Packing Problem (BPP). The BPP is to find the minimum numbers of bins needed to pack a given set of items of known sizes so that they do not exceed the capacity B of each bin. In the CCBP, we are g ..."
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Abstract. The online Class Constrained Bin Packing problem (CCBP) is one of variant version of the Bin Packing Problem (BPP). The BPP is to find the minimum numbers of bins needed to pack a given set of items of known sizes so that they do not exceed the capacity B of each bin. In the CCBP, we are given bins of capacity B with C compartments and n items of Q different classes, each item i is belong to 1,2,…,n with class qi and si. The CCBP is to pack the items into bins, where each bin contains at most Q different classes and has total items size at most B. This CCBP is known to be NPhard combinatorial optimization problems. In this paper, we used an ant colony optimization (ACO) approach with a simple but very effective local search algorithm to resolve this NPhard problem. After the experimental design, limited computational results show the efficiency of this scheme. It is also shown that the ACO approach can outperform some existing methods, whereas the hybrid approach can compete with the known solution methods.