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.

Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks

Abstract: The minimum range assignment problem consists of assigning transmission ranges to the stations of a multi-hop packet radio network so as to minimize the total power consumption provided that the transmission range assigned to the stations ensures the strong connectivity of the network (i.e. each station can communicate with any other station by multi-hop transmission). The complexity of this optimization problem was studied by Kirousis, Kranakis, Krizanc, and Pelc (1997). In particular, they proved that, when the stations are located in a 3-dimensional Euclidean space, the problem is NP-hard and admits a 2-approximation algorithm. On the other hand, they left the complexity of the 2-dimensional case as an open problem.

Optimal relay assignment for cooperative communications

Abstract: Recently, cooperative communications, in the form of keeping each node with a single antenna and having a node exploit a relay node's antenna, is shown to be a promising approach to achieve spatial diversity. Under this communication paradigm, the choice of relay node plays a significant role in the overall system performance. In this paper, we study the relay node assignment problem in a network environment, where multiple source-destination pairs compete for the same pool of relay nodes in the network. The main contribution of this paper is the development of a polynomial time algorithm to solve this problem. A key idea in this algorithm is a "linear marking" mechanism, which is able to offer a linear complexity for each iteration. We give a formal proof of optimality for this algorithm. We also show several attractive properties associated with this algorithm.

Tight Approximation Algorithms for Maximum Separable Assignment Problems

Abstract: A separable assignment problem ( SAP ) is defined by a set of bins and a set of items to pack in each bin; a value, fij, for assigning item j to bin i; and a separate packing constraint for each bin---i.e., for each bin, a family of subsets of items that fit in to that bin. The goal is to pack items into bins to maximize the aggregate value. This class of problems includes the maximum generalized assignment problem ( GAP )1 and a distributed caching problem (DCP) described in this paper. Given a β-approximation algorithm for finding the highest value packing of a single bin, we give A polynomial-time LP-rounding based ((1-1/e)β)-approximation algorithm. A simple polynomial-time local search (β/(β + 1)-e)-approximation algorithm, for any e > 0. Therefore, for all examples of SAP that admit an approximation scheme for the single-bin problem, we obtain an LP-based algorithm with (1-1/e-e)-approximation and a local search algorithm with (½-e)-approximation guarantee. Furthermore, for cases in which the subproblem admits a fully polynomial approximation scheme (such as for GAP ), the LP-based algorithm analysis can be strengthened to give a guarantee of 1-1/e. The best previously known approximation algorithm for GAP is a ½-approximation by Shmoys and Tardos and Chekuri and Khanna. Our LP algorithm is based on rounding a new linear programming relaxation, with a provably better integrality gap. To complement these results, we show that SAP and DCP cannot be approximated within a factor better than 1-1/e unless NP ⊆ DTIME(nO(log log n)), even if there exists a polynomial-time exact algorithm for the single-bin problem. We extend the (1-1/e)-approximation algorithm to a constant-factor approximation algorithms for a nonseparable assignment problem with applications in maximizing revenue for budget-constrained combinatorial auctions and the AdWords assignment problem. We generalize the local search algorithm to yield a ½-e approximation algorithm for the maximum k-median problem with hard capacities.

Transit route and frequency design:Bi-level modeling and hybrid artificial bee colony algorithm approach

Abstract: This paper proposes a bi-level transit network design problem where the transit routes and frequency settings are determined simultaneously. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the number of passenger transfers, and the lower-level problem is the transit assignment problem with capacity constraints. A hybrid artificial bee colony (ABC) algorithm is developed to solve the bi-level problem. This algorithm relies on the ABC algorithm to design route structures and a proposed descent direction search method to determine an optimal frequency setting for a given route structure. The descent direction search method is developed by analyzing the optimality conditions of the lower-level problem and using the relationship between the lower- and upper-level objective functions. The step size for updating the frequency setting is determined by solving a linear integer program. To efficiently repair route structures, a node insertion and deletion strategy is proposed based on the average passenger demand for the direct services concerned. To increase the computation speed, a lower bound of the objective value for each route design solution is derived and used in the fitness evaluation of the proposed algorithm. Various experiments are set up to demonstrate the performance of our proposed algorithm and the properties of the problem.