Parametric Shortest-Path Algorithms via Tropical Geometry
نویسندگان
چکیده
We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms tropical geometry. Applications include shortest paths traffic networks with variable link travel times.
منابع مشابه
ALGORITHMS FOR BIOBJECTIVE SHORTEST PATH PROBLEMS IN FUZZY NETWORKS
We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the sing...
متن کاملTwo-phase Algorithms for the Parametric Shortest Path Problem
A parametric weighted graph is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edgeweighted graph. Parametric weighted graph problems are generalizations of weighted graph problems, and arise in various natural scenarios. Parametric weighted graph algorithms consist of two phases. A preproc...
متن کاملFaster parametric shortest path and minimum-balance algorithms
We use Fibonacci heaps to improve a parametric shortest path algorithm of Karp and Orlin, and we combine our algorithm and the method of Schneider and Schneider’s minimum-balance algorithm to obtain a faster minimum-balance algorithm. For a graph with n vertices and m edges, our parametric shortest path algorithm and our minimum-balance algorithm both run in O(nm + n logn) time, improved from O...
متن کاملK shortest path algorithms
This paper is focussed on algorithms to solve the k-shortest path problem. Three codes were described and compared on rand and grid networks using random generators available on http://www.dis.uniroma1.it/∼challenge9 Codes were also tested on the USA road networks available on the same URL address. One million paths were ranked in less than 3 seconds on random instances with 10 000 nodes and 10...
متن کاملEngineering Shortest Path Algorithms
In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths. In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra’s shortest path algorithm. In this context, we show that studying heuristics that are efficient in practice can yield interesting clues to the combinatorial properties...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2022
ISSN: ['0364-765X', '1526-5471']
DOI: https://doi.org/10.1287/moor.2021.1199