On the Existence of Truthful Mechanisms for the Minimum-Cost Approximate Shortest-Paths Tree Problem

2006 ◽  
pp. 295-309 ◽  
Author(s):  
Davide Bilò ◽  
Luciano Gualà ◽  
Guido Proietti
Keyword(s):  
Shortest Paths ◽  
Minimum Cost

scholarly journals The Capacity Expansion Path Problem in Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jianping Li ◽  
Juanping Zhu
Keyword(s):  
Shortest Path ◽  
Polynomial Algorithm ◽  
Shortest Paths ◽  
Minimum Cost ◽  
Capacity Expansion ◽  
Shortest Path Problem ◽  
Strongly Polynomial Algorithm ◽  
Minimum Number ◽  
Expansion Path ◽  
Strongly Polynomial

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. For the minimum number arc capacity expansion path problem (MN-CEP), we give a strongly polynomial algorithm based on the dynamic programming. For the minimum-cost capacity expansion shortest path problem (MCESP), we give a strongly polynomial algorithm by constructing a shortest paths network.

Assigning Traffic over Essentially-Least-Cost Paths

1996 ◽  
Vol 1556 (1) ◽  
pp. 1-7 ◽  
Author(s):  
David T. Hunt ◽  
Alain L. Kornhauser
Keyword(s):  
Shortest Paths ◽  
Minimum Cost ◽  
Equilibrium Path ◽  
Least Cost Path ◽  
Single Origin ◽  
Cost Paths ◽  
Least Cost Paths ◽  
Assignment Models ◽  
Single Path ◽  
Predetermined Number

The concept of a least-cost path is generalized. The simplest of all traffic assignment models assumes that all trip makers from a single origin-destination (O-D) pair take a single path, for example, the minimum cost path or the equilibrium path. However, in many applications, it is observed that trips from a single O-D do not all take the same path. It is not difficult to imagine commuters from a large residential area using different routes to travel to a common workplace simply because each has a different disutility function. In reality no two routes have exactly the same cost; however, when modeled deterministically as network graphs, these graphs invariably have O-Ds with degenerate (multiple) shortest paths. The ability to measure the “best” route should also be seriously questioned. Given the level of uncertainty that exists in any link attribute, the variance of the accumulated uncertainty of that attribute over any given route can easily be such as to make many routes statistically indistinguishable from the deterministic best route. An algorithm for generating the set of paths that are essentially indistinguishable from the least-cost path is presented. These paths are constructed from the set of “locally acceptable” detours that are within a given cost threshold. This is different from the classic “k” least-cost path problem in that it operates on a cost threshold as opposed to a predetermined number of paths. Methods are then presented for assigning traffic to this subnetwork of essentially-least-cost paths.

Optimizing bipartite matching in real-world applications by incremental cost computation

2021 ◽  
Vol 14 (7) ◽  
pp. 1150-1158
Author(s):  
Tenindra Abeywickrama ◽  
Victor Liang ◽  
Kian-Lee Tan
Keyword(s):  
Real World ◽  
Shortest Paths ◽  
Minimum Cost ◽  
Wait Time ◽  
Optimal Assignment ◽  
Real World Data ◽  
Bipartite Matching ◽  
Lower Bounding ◽  
Real World Applications ◽  
The Impact

The Kuhn-Munkres (KM) algorithm is a classical combinatorial optimization algorithm that is widely used for minimum cost bipartite matching in many real-world applications, such as transportation. For example, a ride-hailing service may use it to find the optimal assignment of drivers to passengers to minimize the overall wait time. Typically, given two bipartite sets, this process involves computing the edge costs between all bipartite pairs and finding an optimal matching. However, existing works overlook the impact of edge cost computation on the overall running time. In reality, edge computation often significantly outweighs the computation of the optimal assignment itself, as in the case of assigning drivers to passengers which involves computation of expensive graph shortest paths. Following on from this observation, we observe common real-world settings exhibit a useful property that allows us to incrementally compute edge costs only as required using an inexpensive lower-bound heuristic. This technique significantly reduces the overall cost of assignment compared to the original KM algorithm, as we demonstrate experimentally on multiple real-world data sets, workloads, and problems. Moreover, our algorithm is not limited to this domain and is potentially applicable in other settings where lower-bounding heuristics are available.

scholarly journals A Comprehensive Comparison of Label Setting Algorithm and Dynamic Programming Algorithm in Solving Shortest Path Problems

2021 ◽  
Vol 13 (5) ◽  
pp. 14
Author(s):  
Douglas Yenwon Kparib ◽  
John Awuah Addor ◽  
Anthony Joe Turkson
Keyword(s):  
Dynamic Programming ◽  
Shortest Path ◽  
Shortest Paths ◽  
Dynamic Programming Algorithm ◽  
Minimum Cost ◽  
Programming Algorithm ◽  
Shortest Path Problems ◽  
Comprehensive Comparison ◽  
Paper Label ◽  
Label Setting Algorithm

In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10  and  1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.

scholarly journals Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bingwu Zhang ◽  
Xiucui Guan ◽  
Chunyuan He ◽  
Shuguo Wang
Keyword(s):  
Polynomial Time ◽  
Shortest Path ◽  
Hamming Distance ◽  
Programming Model ◽  
Greedy Algorithms ◽  
Shortest Paths ◽  
Weighted Graph ◽  
Minimum Cost ◽  
Strongly Polynomial Time ◽  
Strongly Polynomial

In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are upper bounded by given values. The SPIUH problem on arborescent network is formulated as a 0-1 integer programming model. Some strongly polynomial time algorithms are designed for the problems on some special arborescent networks. Firstly, two greedy algorithms are proposed for problems on chain networks and special star-tree networks, respectively. Secondly, a strongly polynomial time algorithm is presented for the problem with a single source and constrained paths. Finally, a heuristic algorithm and its computational experiments are given for the SPIUH problem on general graphs.

A generalized fuzzy cost efficiency model

2020 ◽  
Vol 54 (6) ◽  
pp. 1775-1791
Author(s):  
Nazila Aghayi ◽  
Samira Salehpour
Keyword(s):  
Cost Efficiency ◽  
Minimum Cost ◽  
Extensive Literature ◽  
Data Envelopment ◽  
Fuzzy Environment ◽  
Decision Making Unit ◽  
Production Possibility Set ◽  
Fuzzy Cost ◽  
The Cost ◽  
Generalized Cost

The concept of cost efficiency has become tremendously popular in data envelopment analysis (DEA) as it serves to assess a decision-making unit (DMU) in terms of producing minimum-cost outputs. A large variety of precise and imprecise models have been put forward to measure cost efficiency for the DMUs which have a role in constructing the production possibility set; yet, there’s not an extensive literature on the cost efficiency (CE) measurement for sample DMUs (SDMUs). In an effort to remedy the shortcomings of current models, herein is introduced a generalized cost efficiency model that is capable of operating in a fuzzy environment-involving different types of fuzzy numbers-while preserving the Farrell’s decomposition of cost efficiency. Moreover, to the best of our knowledge, the present paper is the first to measure cost efficiency by using vectors. Ultimately, a useful example is provided to confirm the applicability of the proposed methods.

Main approaches to estimating the cost of shareholder equity of oil and gas producers

2020 ◽  
Vol 26 (3) ◽  
pp. 685-697
Author(s):  
O.V. Shimko
Keyword(s):  
Oil And Gas ◽  
Oil Prices ◽  
Minimum Cost ◽  
Free Cash Flow ◽  
Annual Reports ◽  
Comparative Approach ◽  
Economic Activities ◽  
Advantages And Disadvantages ◽  
Oil And Gas Producers ◽  
The Cost

Subject. The study analyzes generally accepted approaches to assessing the value of companies on the basis of financial statement data of ExxonMobil, Chevron, ConocoPhillips, Occidental Petroleum, Devon Energy, Anadarko Petroleum, EOG Resources, Apache, Marathon Oil, Imperial Oil, Suncor Energy, Husky Energy, Canadian Natural Resources, Royal Dutch Shell, Gazprom, Rosneft, LUKOIL, and others, for 1999—2018. Objectives. The aim is to determine the specifics of using the methods of cost, DFC, and comparative approaches to assessing the value of share capital of oil and gas companies. Methods. The study employs methods of statistical analysis and generalization of materials of scientific articles and official annual reports on the results of financial and economic activities of the largest public oil and gas corporations. Results. Based on the results of a comprehensive analysis, I identified advantages and disadvantages of standard approaches to assessing the value of oil and gas producers. Conclusions. The paper describes pros and cons of the said approaches. For instance, the cost approach is acceptable for assessing the minimum cost of small companies in the industry. The DFC-based approach complicates the reliability of medium-term forecasts for oil prices due to fluctuations in oil prices inherent in the industry, on which the net profit and free cash flow of companies depend to a large extent. The comparative approach enables to quickly determine the range of possible value of the corporation based on transactions data and current market situation.

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