Maximum Multicommodity Flow with Intermediate Storage

The multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in the maximization of flow values. In this paper, we introduce the maximum static as well as maximum dynamic multicommodity flow problems with intermediate storage. We present polynomial and pseudopolynomial time algorithms for the former and latter problems, respectively. We also present the solution procedures to these problems in contraflow network having symmetric as well as asymmetric arc transit times. We transform the solutions in continuous-time settings by using natural transformation.

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Relaxation methods for the strictly convex multicommodity flow problem with capacity constraints on individual commodities

Networks ◽

10.1002/net.3230200405 ◽

1990 ◽

Vol 20 (4) ◽

pp. 409-426 ◽

Cited By ~ 4

Author(s):

Hiroshi Nagamochi ◽

Masao Fukushima ◽

Toshihide Lbaraki

Keyword(s):

Flow Problem ◽

Capacity Constraints ◽

Multicommodity Flow ◽

Relaxation Methods ◽

Strictly Convex ◽

Multicommodity Flow Problem

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Approximate Algorithms for Continuous-Time Quickest Multi-Commodity Contraflow Problem

The Nepali Mathematical Sciences Report ◽

10.3126/nmsr.v37i1-2.34068 ◽

2020 ◽

Vol 37 (1-2) ◽

pp. 30-46

Author(s):

Shiva Prakash Gupta ◽

Durga Prasad Khanal ◽

Urmila Pyakurel ◽

Tanka Nath Dhamala

Keyword(s):

Approximation Algorithms ◽

Polynomial Time ◽

Continuous Time ◽

Flow Problem ◽

Capacity Constraints ◽

Approximate Algorithms ◽

Optimal Solutions ◽

Commodity Flow ◽

Flow Problems

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are computationally hard. The outbound lane capacities can be increased through reverting the orientation of lanes towards the demand nodes. We present two approximation algorithms by introducing partial contraow technique in the continuous-time quick estmulti-commodity ow problem: one polynomial-time with the help of length-bounded flow and another FPTAS by using _-condensed time-expanded graph. Both algorithms reverse only necessary arc capacities to get the optimal solutions and save unused arc capacities which may be used for other purposes.

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