Successive Shortest Path Algorithm Research Articles

System optimum dynamic traffic assignment with departure time choice on two-terminal networks

ABSTRACTThis paper addresses the system optimum dynamic traffic assignment (SO-DTA) problem with departure time choice on a two-terminal network, where the travel cost consists of travel time and an early schedule delay cost. Under a certain condition, we show that SO-DTA reduces to the latest departure earliest arrival flow (LDEAF), and hence methodologies of LDEAF can be used to study SO-DTA. A successive shortest path (SSP) algorithm is used to solve the LDEAF problem. The benefit is that the SSP algorithm involves only the shortest path computations on a static network. System marginal costs, externalities and dynamic user equilibrium tolls are analyzed in the LDEAF context, and used to provide a better understanding of the SO-DTA problem characteristics. Further, the study findings can be used for the morning commute problem as it is a special case of the SO-DTA problem on a two-terminal network.

Reduction of the asymptotic complexity of the assignment problem

The assignment problem belongs to an extensive class of managerial decision-making tasks. One of the urgent tasks related to this class is the problem of effectively combining various streams (resources). The main purpose of the method modifications is to reduce the asymptotic complexity and to consider the specifics of the subject area. The article describes the solution of the assignment problem on a bipartite sparse graph. The main purpose of the method modifications is to reduce the asymptotic complexity and to consider the specifics of the subject area. A modification of the Hungarian method is proposed. The method is based on the successive shortest path algorithm and Dijkstra’s bidirectional search algorithm. The modification led to a decrease in the asymptotic complexity of the problem.

Smoothed Analysis of the Successive Shortest Path Algorithm

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudopolynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that both the problem and the algorithms are well understood. However, some of the algorithms' running times observed in empirical studies contrast the running times obtained by worst-case analysis not only in the order of magnitude but also in the ranking when compared to each other. For example, the successive shortest path (SSP) algorithm, which has an exponential worst-case running time, seems to outperform the strongly polynomial minimum-mean cycle canceling algorithm. To explain this discrepancy, we study the SSP algorithm in the framework of smoothed analysis and establish a bound of $O(mn\phi)$ for the number of iterations, which implies a smoothed running time of $O(mn\phi (m + n\log n))$, where $n$ and $m$ denote the number of nodes and edges, respectively, and $\phi$ is a measure for the amount of random noise. This shows that worst-case instances for the SSP algorithm are not robust and unlikely to be encountered in practice. Furthermore, we prove a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$ for the number of iterations of the SSP algorithm, showing that the upper bound cannot be improved for $\phi = \Omega(n)$.

Optimal Water System Operation Using Graph Theory Algorithms

The water system minimum-cost flow problem is solved using the successive shortest path (SSP), graph theory algorithm, by representing the network as a directed graph. The graph nodes represent water sources, junctions, tanks and consumers. The edges represent pipes, pumping stations water tanks. The successive shortest path algorithm is applied to the graph ending when max flow limitation is fulfilled between the sources and sink nodes, returning minimal operating costs. A simple 24 h water system is examined using the proposed graph representation. The results are compared to the results of numeration and standard linear programing solver.

Minimum cost time-varying network flow problems

This paper deals with a general minimum cost dynamic flow problem in a discrete time model with time-varying transit times, transit costs, transit capacities, storage costs, and storage capacities. For this problem, an algorithm of time complexity O(V nT(n+T)) is presented, where V is an upper bound on the total supply, n is the number of nodes, and T denotes the given time horizon of the dynamic flow problem. The algorithm is a discrete-time version of the successive shortest path algorithm.

Outsourcing prioritized warranty repairs

Purpose – To consider the problem of outsourcing warranty repairs to outside vendors when items have priorities in service.Design/methodology/approach – The repair allocation problem is formulated as a convex minimum‐cost network flow problem and solve it by the successive shortest path algorithm. The computation issues involved with the problem are also discussed.Findings – Examples are provided to illustrate the cost benefits achieved due to the priority structure.Research limitations/implications – The research uses a closed static allocation model. Future research efforts can expand our model by considering a dynamic allocation method or an open population model.Practical implications – The paper can be a valuable resource to warranty managers who make decisions regarding the negotiations of warranty contracts and the allocation of items to outside repair vendors.Originality/value – A warranty manager can apply our results to receive insight on the value of giving priority in service to special custom...

Polynomial combinatorial optimization methods for analysing the ground states of disordered systems

We discuss the application of polynomial combinatorial optimization algorithms to extract the universal zero-temperature properties of various disordered systems. Dijkstras algorithm is used for models of non-directed elastic lines on general regular graphs with isotropically correlated random potentials. The successive shortest path algorithm for minimum-costflow problems is applied for the study of ground state properties and the entanglement of many elastic lines in a disordered environment and the disorder-induced loop percolation transition in a vortex glass model. The preflow-push algorithm for minimum-cut–maximum-flow problems is used for the investigation of a roughening transition occurring in a model for elastic manifolds in a periodic potential in the presence of point disorder.

Capacity scaling algorithm for scalable M-convex submodular flow problems

An M-convex function is a nonlinear discrete function defined on integer points introduced by Murota in 1996, and the M-convex submodular flow problem is one of the most general frameworks of efficiently solvable combinatorial optimization problems. It includes the minimum cost flow and the submodular flow problems as its special cases. In this paper, we first devise a successive shortest path algorithm for the M-convex submodular flow problem. We then propose an efficient algorithm based on a capacity scaling framework for the scalable M-convex submodular flow problem. Here an M-convex function [Formula: See Text] is said to be scalable if [Formula: See Text] is also M-convex for any positive integer [Formula: See Text] and any integer vector b.

New scaling algorithms for the assignment and minimum mean cycle problems

In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recentauction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is successively reduced to zero. On a network with 2n nodes,m arcs, and integer arc costs bounded byC, the algorithm runs in O(\(\sqrt n \) m log(nC)) time and uses very simple data structures. This time bound is comparable to the time taken by Gabow and Tarjan's scaling algorithm, and is better than all other time bounds under thesimilarity assumption, i.e.,C = O(n k) for somek. We next consider the minimum mean cycle problem. Themean cost of a cycle is defined as the cost of the cycle divided by the number of arcs it contains. Theminimum mean cycle problem is to identify a cycle whose mean cost is minimum. We show that by using ideas of the assignment algorithm in an approximate binary search procedure, the minimum mean cycle problem can also be solved in O(\(\sqrt n \) m lognC) time. Under the similarity assumption, this is the best available time bound to solve the minimum mean cycle problem.