We consider an off-line modified delayed-start LPT algorithm that optimally schedules the first longest 7 jobs and the remaining jobs according to the LPT rule on two identical parallel *** show that this algorithm ha...
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We consider an off-line modified delayed-start LPT algorithm that optimally schedules the first longest 7 jobs and the remaining jobs according to the LPT rule on two identical parallel *** show that this algorithm has a sharper tight worst-case ratio bound 1 + 1/81 than the traditional LPT algorithm for the sum of squares of machine completion times minimization problem.
Given a finite family of sets, Hall's classical marriage theorem provides a necessary and sufficient condition for the existence of a system of distinct representatives for the sets in the family. Here we extend t...
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ISBN:
(纸本)9781450320313
Given a finite family of sets, Hall's classical marriage theorem provides a necessary and sufficient condition for the existence of a system of distinct representatives for the sets in the family. Here we extend this result to a geometric setting: given a finite family of objects in the Euclidean space (e.g., convex bodies), we highlight a sufficient condition for the existence of a system of distinct representatives for the objects that are also distant from each other. For a wide variety of geometric objects, this sufficient condition is also necessary in an asymptotic sense (i.e., apart from constant factors, the inequalities are best possible). Our methods are constructive and lead to efficient algorithms for computing such representatives.
We investigate a class of single-item multi-supply auctions (including digital goods auctions with unlimited supply) with bidders who have identity-based negative externalities. In such an auction, each bidder has a s...
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We investigate a class of single-item multi-supply auctions (including digital goods auctions with unlimited supply) with bidders who have identity-based negative externalities. In such an auction, each bidder has a set of competitors. Her private valuation from winning an item decreases with the number of her winning competitors. Negative externalities are prevalent in many applications, in which the auctioned goods play a role in future interactions among the auction's participants, such as patent licensing and sponsored search auctions. However, the development of auctions with such externalities is stymied by the computational difficulty of the underlying welfare maximization allocation problem; even without consideration of truthfulness, the problem of social welfare maximization with general competition relations is NP-hard and even hard to approximate within a constant factor (unless P=NP). In this work, we design polynomial time and strategy-proof mechanisms under different restrictions on the underlying competition graph structure. Our results can be summarized as follows. (1) When each bidder has only one competitor, we propose a truthful and welfare maximizing mechanism. (2) We design a truthful and (1 + ε )-approximation mechanism when the underlying competition graph is planar. (3) We give two truthful mechanisms when bidders have ar- bitrary competition relations, with welfare approximation ratio (n/ log n) and [(d + 1)/3], respectively, where d is the maximum degree of the "undirected" competition graph.
We consider the lifetime optimization problem for multicasting inwireless ad hoc networks, in which each node is equipped with a directional antennaand has limited energy supplies. In this paper, we propose a new dist...
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ISBN:
(纸本)9783540898931
We consider the lifetime optimization problem for multicasting inwireless ad hoc networks, in which each node is equipped with a directional antennaand has limited energy supplies. In this paper, we propose a new distributedalgorithm, whose performance in terms of providing long-lived multicasttree is guaranteed by our theoretical analysis. We prove that its approximationratio is bounded by a finite number. In particular, the derived upper bound in aclosed form shows that the algorithm can achieve global optimal in some *** real performance of this new proposed algorithm is also evaluated usingsimulation studies and the experimental results show that it outperforms otherdistributed algorithms.
As a common task in the fields of bioinformatics, enrichment analysis aims to investigate the functional association between a gene list of interest which often derived from biological experiments, and specific gene s...
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ISBN:
(纸本)9781510821224
As a common task in the fields of bioinformatics, enrichment analysis aims to investigate the functional association between a gene list of interest which often derived from biological experiments, and specific gene sets in a large database. The core problem of enrichment analysis can be characterized as a two-objective optimization problem. In this paper, we formulated the multiple gene sets enrichment problem into a variant of the set cover problem, named enrichment set cover problem, and designed four approximation algorithms to solve the NP-hard enrichment set cover problem. The performance of proposed approximation algorithms were analyzed theoretically and evaluated on the data sets from real biological databases.
In democratic elections, malicious agents may attempt to control elections to achieve their own goals. To guarantee impartiality, it is necessary to protect the election outcomes from control. In this paper, we consid...
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In democratic elections, malicious agents may attempt to control elections to achieve their own goals. To guarantee impartiality, it is necessary to protect the election outcomes from control. In this paper, we consider how to protect election outcome from control using minimal resources. We assume malicious agents attempt to prevent a specific candidate from winning a democratic election with plurality rule through denial-of-service (deletion) attacks on voter groups (e.g., polling places). First, we show that the problem is NP-hard. Second, we propose a (|C|-1)-approximation algorithm for the problem, where |C| is the number of candidates. Finally, we validate the efficiency of our approximation algorithm based on simulation experiments.
In this paper, we address the scheduling model with discretely compressible release dates, where processing any job with a compressed release date incurs a corresponding compression cost. We consider the following pro...
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In this paper, we address the scheduling model with discretely compressible release dates, where processing any job with a compressed release date incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible release dates to minimize the sum of makespan plus total compression cost. We show its NP-hardness, and design an approximation algorithm with worst-case performance ratio 2.
We study a variant of the reentrant shop problem of minimizing makespan in one hub machine At, and two machine centers M2 and M3 (each center consists of some identical machines). In the problem, each job has five...
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We study a variant of the reentrant shop problem of minimizing makespan in one hub machine At, and two machine centers M2 and M3 (each center consists of some identical machines). In the problem, each job has five operations, where the first, the third and the fifth operation must be performed on hub machine Mt, the second operation can be performed on any one machine in M2 and the forth operation can be performed on any one machine in My We show the problem is strongly NP-hard, which motivates us to design approximation algorithms. We give a fully polynomial time approximation scheme (FPTAS) for the job-machine assignment decision in M2 and M3. Based on the FPTAS, we then provide a mixed integer linear programming (MILP) to schedule job operations optimally.
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-time approximation 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 approximation scheme, i.e. an algorithm of approximation ratio 1+ epsilon for epsilon > 0 , with an improved running time only single exponential in 1/epsilon .
The classical Load Balancing Problem (LBP) is to map tasks to processors so as to minimize the maximum load. Solving the LBP successfully would lead to better utilization of resources and better performance. The LBP h...
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The classical Load Balancing Problem (LBP) is to map tasks to processors so as to minimize the maximum load. Solving the LBP successfully would lead to better utilization of resources and better performance. The LBP has been proven to be NP-hard, thus generating the exact solutions in a tractable amount of time becomes infeasible when the problems become *** present a new nature-inspired approximation algorithm based on the Particle Mechanics (PM) model to compute in parallel approximate *** solutions for LBPs. Just like other Nature-inspired algorithms (NAs) drawing from observations of physical processes that occur in nature, the PM algorithm is inspired by physical models of particle kinematics and dynamics. The PM algorithm maps the classical LBP to the movement of particles in a *** by a corresponding mathematical model in which all particles move according to certain *** rules until reaching a stable state. By anti-mapping the stable state, the solution to LBP can be obtained.
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