Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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30 Nov 2008
TL;DR: The problem of optimal static period assignment for multiple independent control tasks executing on the same CPU is considered, arguing that the control delay has a large impact on the control performance, and the delay is estimated using an approximate response-time analysis.
Abstract: We consider the problem of optimal static period assignment for multiple independent control tasks executing on the same CPU. Previous works have assumed that the control performance can be expressed as a function of the sampling rate only. Arguing that the control delay has a large impact on the control performance, in this work we include the control delay in the cost function. The delay is estimated using an approximate response-time analysis. Assuming linear cost functions for the controllers then allows us to solve the optimal period assignment problem analytically. The performance improvements over previous methods are verified in evaluations on synthetic task sets as well as detailed co- simulations of the controllers, the plants, and the scheduler.
131 citations
01 Oct 2001
TL;DR: A probabilistic solution to this range assignment problem achieves substantial energy savings and establishes lower and upper bounds on the probability of connectedness for the one-dimensional case.
Abstract: In this paper we consider the following problem for ad hoc networks: assume that n nodes are distributed in a d-dimensional region, with 1≤d≤3, and assume that all the nodes have the same transmitting range r; how large must r be to ensure that the resulting network is strongly connected? We study this problem by means of a probabilistic approach, and we establish lower and upper bounds on the probability of connectedness. For the one-dimensional case, these bounds allow us to determine a suitable magnitude of r for a given number of nodes and displacement region size. In an alternate formulation, the bounds allow us to calculate how many nodes must be distributed should the transmitting range be fixed. Finally, we investigate the required magnitude of r in the two- and three-dimensional cases through simulation. Based on the bounds provided and on the simulation analysis, we conclude that, as compared to the deterministic case, a probabilistic solution to this range assignment problem achieves substantial energy savings. A number of other potential uses for our analyses are discussed as well
131 citations
TL;DR: Close connections are demonstrated between mean field theory methods and other approaches, in particular, barrier function and interior point methods, for obtaining approximate solutions to optimization problems.
Abstract: In recent years there has been significant interest in adapting techniques from statistical physics, in particular mean field theory, to provide deterministic heuristic algorithms for obtaining approximate solutions to optimization problems. Although these algorithms have been shown experimentally to be successful there has been little theoretical analysis of them. In this paper we demonstrate connections between mean field theory methods and other approaches, in particular, barrier function and interior point methods. As an explicit example, we summarize our work on the linear assignment problem. In this previous work we defined a number of algorithms, including deterministic annealing, for solving the assignment problem. We proved convergence, gave bounds on the convergence times, and showed relations to other optimization algorithms.
128 citations
TL;DR: The paper considers the classic linear assignment problem with a min-sum objective function, and the most efficient and easily available codes for its solution, and selects eight codes.
128 citations
TL;DR: Daily traffic assignments to a large-scale road network are described for Build and No-Build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley Region and reveal that a relative gap of 0.01% is required to assure that the traffic assignments are sufficiently converged to achieve link flow stability.
Abstract: Daily traffic assignments to a large-scale road network are described for Build and No-Build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley Region. The road network consists of 39,800 links connecting 1,510 zones. The user-equilibrium traffic assignment problem was solved with a new algorithm called origin-based assignment (OBA), which can achieve highly converged solutions with reasonable computing effort. Following a description of the user-equilibrium traffic assignment problem and the OBA algorithm, the stability of link flow differences between the two scenarios in the vicinity of the proposed ramps are examined over a broad range of assignment convergence levels. Then, link flow differences over this range of convergence levels are compared to link flow differences between two very highly converged solutions. Examination of the findings reveals in the authors' view that a relative gap of 0.01% (0.0001) is required to assure that the traffic assignments are sufficiently converged to achieve link flow stability. These convergence levels are then interpreted in terms of the number of Frank-Wolfe iterations needed to achieve comparable relative gaps, as well as the computational effort required.
128 citations