1,271 research outputs found
Some recent results in the analysis of greedy algorithms for assignment problems
We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems
Efficient Algorithms for Scheduling Moldable Tasks
We study the problem of scheduling independent moldable tasks on
processors that arises in large-scale parallel computations. When tasks are
monotonic, the best known result is a -approximation
algorithm for makespan minimization with a complexity linear in and
polynomial in and where is
arbitrarily small. We propose a new perspective of the existing speedup models:
the speedup of a task is linear when the number of assigned
processors is small (up to a threshold ) while it presents
monotonicity when ranges in ; the bound
indicates an unacceptable overhead when parallelizing on too many processors.
For a given integer , let . In this paper, we propose a -approximation algorithm for makespan minimization with a
complexity where
(). As
a by-product, we also propose a -approximation algorithm for
throughput maximization with a common deadline with a complexity
Very Large-Scale Neighborhoods with Performance Guarantees for Minimizing Makespan on Parallel Machines
We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima
On the Value of Job Migration in Online Makespan Minimization
Makespan minimization on identical parallel machines is a classical
scheduling problem. We consider the online scenario where a sequence of
jobs has to be scheduled non-preemptively on machines so as to minimize the
maximum completion time of any job. The best competitive ratio that can be
achieved by deterministic online algorithms is in the range .
Currently no randomized online algorithm with a smaller competitiveness is
known, for general .
In this paper we explore the power of job migration, i.e.\ an online
scheduler is allowed to perform a limited number of job reassignments.
Migration is a common technique used in theory and practice to balance load in
parallel processing environments. As our main result we settle the performance
that can be achieved by deterministic online algorithms. We develop an
algorithm that is -competitive, for any , where
is the solution of a certain equation. For , and
. Here is the lower branch of the Lambert function.
For , the algorithm uses at most migration operations. For
smaller , to operations may be performed. We complement this
result by a matching lower bound: No online algorithm that uses job
migrations can achieve a competitive ratio smaller than . We finally
trade performance for migrations. We give a family of algorithms that is
-competitive, for any . For , the strategy uses at
most job migrations. For , at most migrations are used.Comment: Revised versio
Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines
We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima.operations research and management science;
Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems
In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons
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