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Online competitive algorithms for maximizing weighted throughput of unit jobs
 In Proc. 21st Symp. on Theoretical Aspects of Computer Science (STACS
, 2004
"... Abstract. We study an online buffer management problem for networks supporting QualityofService (QoS) applications. Packets with different QoS values arrive at a network switch and are to be sent along an outgoing link. Due to overloading conditions, some packets have to be dropped. The objective ..."
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Cited by 17 (3 self)
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Abstract. We study an online buffer management problem for networks supporting QualityofService (QoS) applications. Packets with different QoS values arrive at a network switch and are to be sent along an outgoing link. Due to overloading conditions, some packets have to be dropped. The objective is to maximize the total value of packets that are sent. We formulate this as an online scheduling problem for unitlength jobs, where each job is specified by its release time, deadline, and a nonnegative weight (QoS value). The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs. We first give a randomized algorithm RMix with competitive ratio of e/(e − 1) ≈ 1.582. This is the first algorithm for this problem with competitive ratio smaller than 2. Then we consider sbounded instances where the span of each job (deadline minus release time) is at most s. We give a 1.25competitive randomized algorithm for 2bounded instances, matching the known lower bound. We give a deterministic algorithm Edfα, whose competitive ratio on sbounded instances is at most 2 − 2/s + o(1/s). For 3bounded instances its ratio is φ ≈ 1.618, matching the lower bound. Previously, an upper bound of φ was known for 2bounded instances, and our work extends this result. Next, we consider 2uniform instances, where the span of each job is exactly 2. We prove a lower bound of 4 − 2 √ 2 ≈ 1.172 for randomized algorithms. For deterministic memoryless algorithms, we prove a lower bound of √ 2 ≈ 1.414, matching a known upper bound. Finally, we consider the multiprocessor case and give an 1/(1 − ( M M+1)M)competitive algorithm for M processors. We also show improved lower bounds for the general and 2uniform cases. 1
Better Bounds for Online Load Balancing on Unrelated Machines
"... We study the problem of scheduling permanent jobs on unrelated machines when the objective is to minimize the Lp norm of the machine loads. The problem is known as load balancing under the Lp norm. We present an improved upper bound for the greedy algorithm through simple analysis; this bound is als ..."
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Cited by 14 (1 self)
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We study the problem of scheduling permanent jobs on unrelated machines when the objective is to minimize the Lp norm of the machine loads. The problem is known as load balancing under the Lp norm. We present an improved upper bound for the greedy algorithm through simple analysis; this bound is also shown to be best possible within the class of deterministic online algorithms for the problem. We also address the question whether randomization helps online load balancing under Lp norms on unrelated machines; this is a challenging question which is open for more than a decade even for the L2 norm. We provide a positive answer to this question by presenting the first randomized online algorithms which outperform deterministic ones under any (integral) Lp norm for p = 2,..., 137. Our algorithms essentially compute in an online manner a fractional solution to the problem and use the fractional values to make random choices. The local optimization criterion used at each step is novel and rather counterintuitive: the values of the fractional variables for each job correspond to flows at an approximate Wardrop equilibrium for an appropriately defined nonatomic congestion game. As corollaries of our analysis and by exploiting the relation between the Lp norm and the makespan of machine loads, we obtain new competitive algorithms for online makespan minimization, making progress in another longstanding open problem.
Optimal Online Algorithms for Minimax Resource Scheduling
"... We consider a very general online scheduling problem with an objective to minimize the maximum level of resource allocated. We find a simple characterization of an optimal deterministic online algorithm. We develop further results for two more specific problems, single resource scheduling and hierar ..."
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Cited by 4 (0 self)
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We consider a very general online scheduling problem with an objective to minimize the maximum level of resource allocated. We find a simple characterization of an optimal deterministic online algorithm. We develop further results for two more specific problems, single resource scheduling and hierarchical line balancing. We determine how to compute optimal online algorithms for both problems using linear programming and integer programming, respectively. We show that randomized algorithms can outperform deterministic algorithms, but only if the amount of work done is a nonconcave function of resource allocation.
scheduling
, 2009
"... Pareto simulated annealing and colonial competitive algorithm to solve an offline ..."
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Pareto simulated annealing and colonial competitive algorithm to solve an offline