Uniform Cost Model Research Articles

Reverse 1-maxian problem with keeping existing 1-median

Here we investigate the reverse 1-maxian problem when it is necessary to keep 1-median of a given network. This problem asks to modify the parameters of the network so that the 1-median does not change and the candidate place for 1-maxian improves as much as possible. For the uniform-cost model on a tree graph, an algorithm with $$O(n \log n)$$ time complexity is developed. It is also shown that the problem is solvable in linear time where it is only allowed to increase the vertex weights.

Combinatorial Algorithms for Reverse Selective Undesirable Center Location Problems on Cycle Graphs

This paper deals with a general variant of the reverse undesirable (obnoxious) center location problem on cycle graphs. Given a ‘selective’ subset of the vertices of the underlying cycle graph as location of the existing customers, the task is to modify the edge lengths within a given budget such that the minimum of distances between a predetermined undesirable facility location and the customer points is maximized under the perturbed edge lengths. We develop a combinatorial \(\mathcal {O}(n\log n)\) algorithm for the problem with continuous modifications. For the uniform-cost model, we solve this problem in linear time by an improved algorithm. Furthermore, exact solution methods are proposed for the problem with integer modifications.

Does indirect addressing matter?

In the study of random access machines (RAMs) and the complexities associated with their algorithms, the availability of indirect addressing often creates an analysis obstacle. We show that for RAMs equipped with a sufficiently rich set of basic operations, indirect addressing does not increase computational power, and can be simulated either in linear time or on-line in real time. These results pertain to the uniform cost model and, particularly, assume a unit cost variable shift.

Optimization models for siting water quality monitoring stations in a catchment

A water quality monitoring network (WQMN) must be designed so as to adequately protect the water quality in a catchment. Although a simulated annealing (SA) method was previously applied to design a WQMN, the SA method cannot ensure the solution it obtained is the global optimum. Therefore, two new linear optimization models are proposed in this study to minimize the deviation of the cost values expected to identify the possible pollution sources based on uniform cost (UC) and coverage elimination uniform cost (CEUC) schemes. The UC model determines the expected cost values by considering each sub-catchment being covered by which station, while the CEUC model determines the coverage of each station by eliminating the area covered by any upstream station. The proposed models are applied to the Derchi reservoir catchment in Taiwan. Results show that the global optimal WQMN can be effectively determined by using the UC or CEUC model, for which both results are better than those from the SA method, especially when the number of stations becomes large.

Inverse center location problems

Abstract We investigate the inverse 1-center location problem on trees and outline combinatorial algorithms with time complexity O ( n 2 ) in case that the topology of the tree does not change. In the uniform cost model an improved running time of O ( n log n ) can be obtained. If topology changes occur, the complexity increases by a factor bounded by n . This improves earlier results of Yang and Zhang.

A unified theory of garbage collection

Tracing and reference counting are uniformly viewed as being fundamentally different approaches to garbage collection that possess very distinct performance properties. We have implemented high-performance collectors of both types, and in the process observed that the more we optimized them, the more similarly they behaved - that they seem to share some deep structure. We present a formulation of the two algorithms that shows that they are in fact duals of each other. Intuitively, the difference is that tracing operates on live objects, or "matter", while reference counting operates on dead objects, or "anti-matter". For every operation performed by the tracing collector, there is a precisely corresponding anti-operation performed by the reference counting collector. Using this framework, we show that all high-performance collectors (for example, deferred reference counting and generational collection) are in fact hybrids of tracing and reference counting. We develop a uniform cost-model for the collectors to quantify the trade-offs that result from choosing different hybridizations of tracing and reference counting. This allows the correct scheme to be selected based on system performance requirements and the expected properties of the target application.

Uniform multipaging reduces to paging

Multipaging is the paging problem when more than one page can be requested at each step (Feuerstein, 1997). In the uniform cost model, a paging algorithm is charged for the number of pages loaded from disk to fast memory. In this note, we establish a general reduction from uniform multipaging to paging. As a consequence, we obtain the first strongly competitive randomized algorithm for uniform multipaging.

Assessment of effects and costs of information systems.

Insight into the effects and costs of information systems is becoming increasingly important. A key problem is to provide evidence which is transportable among sites. Transportability demands agreement on how to carry out assessment of information systems. In the VISTA study, three Dutch hospitals developed together an evaluation protocol for the assessment of the effects and costs of the nursing information system VISION. This protocol is based on a quasy-experimental study design allowing filtering for non-VISION influences. The protocol also included a uniform cost model. Based on a cost calculation for the three hospitals, the costs for hospital-wide implementation of VISION in a 445- and 800-bed hospital were extrapolated. VISTA is considered as a trial for application of one evaluation protocol at various sites. It is recommended to extend this national trial to a multi-national one, for instance by applying the cost model more broadly.

Probabilistic analysis of two k-cluster problems

The paper provides a probabilistic analysis of the so-called “strong” linear programming relaxation of two k-clustering problems when the number of points n is large. The analysis is performed for two classical models in facility location, the Euclidian and uniform cost models. For the k-centre problem (for example) we show that with k = o( n/log n), k → ∞, the value of the gap ratio ( z IP − z LP)/ z IP is 0.39 and 1 (respectively) for the two models above. We show also that in both cases branch and bound algorithms that use the strong linear programming relaxation as a bound must almost surely explore a nonpolynomial number of nodes to solve the k-centre problem to optimality. However, simple algorithms based on arbitrary solutions or symmetry will almost surely give solutions arbitrarily close to optimal.

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Abstract The average age of tractors in use in the RSA have increased considerably the past couple of years and quite a number of tractors arc already too old for effective functioning. The factors that farmers do take into account when they consider tractor replacement are analysed and compared with factors that determine optimality of tractor replacement. Although farmers have become reluctant to replace tractors, when they do consider replacement, the most relevant factors are considered. Various models are available for replacement decisions of which two are especially suitable for the development of decision support systems namely multiperiod integer programming and uniform cost models. An interactive representation of the uniform cost model is given. Although this user-specific model is developed for advice to individual farmers an average tractor replacement age of 10 years was obtained in a nonnative study. This replacement age is higher than the age normally obtained with traditional accounting procedures and can be ascribed to the inclusion of the so called “challenger” in the uniform cost model.

Probabilistic Analysis of a Relaxation for the k-Median Problem

This paper provides a probabilistic analysis of the so-called “strong” linear programming relaxation of the k-median problem when the number of points, say n, goes to infinity. The analysis is performed under four classical models in location theory, the Euclidean, network, tree and uniform cost models. For example, we show that, for the Euclidean model and k → ∞, k = o(n/log n), the value of the relaxation is almost surely within 0.3 percent of the optimum k-median value. For the uniform cost model and the same conditions on k, we show that the value of the relaxation is almost surely 50 percent of the optimum k-median value. We also show that, under various assumptions, branch and bound algorithms that use the strong linear programming relaxation as a bound must almost surely expand a nonpolynomial number of nodes to solve the k-median problem to optimality. Finally, we report extensive computational experiments. As predicted by the probabilistic analysis, the relaxation was not as tight for the problem instances drawn from the uniform cost model as for the other models.

An augmenting path algorithm for linear matroid parity

Linear matroid parity generalizes matroid intersection and graph matching (and hence network flow, degree-constrained subgraphs, etc.). A polynomial algorithm was given by Lovasz. This paper presents an algorithm that uses timeO(mn 3), wherem is the number of elements andn is the rank. (The time isO(mn 2.5) using fast matrix multiplication; both bounds assume the uniform cost model). For graphic matroids the time isO(mn 2). The algorithm is based on the method of augmenting paths used in the algorithms for all subcases of the problem.