in the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. in this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. two path inequalities for the node-only interdiction problem are represented. it has been proved that the integrality gap of relaxation of the maximum fl...

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-desigu problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on th...

We consider the QoS-aware Multicommodity Flow problem, a natural generalization of the weighted multicommodity flow problem where the demands and commodity values are elastic to the Quality-ofService characteristics of the underlying network. The problem is fundamental in transportation planning and also has important applications beyond the transportation domain. We provide a FPTAS for the QoS...

We are given a graph G = (V, E) and k " commodities ". Each commodity i has a source s i and a destination t i. The goal is to find an (s i , t i) path in the graph G for every commodity i, while minimizing the maximum congestion along any edge. The latter can be written formally as Minimize congestion C = max e |{i : P i e}|, where P i is the (s i , t i) path of commodity i and e is an edge. I...

Container routing determines how to transport containers from their origins to their destinations in a liner shipping network. Container routing needs to be solved a number of times as a subproblem in tactical-level decision planning of liner shipping operations. Container routing is similar to the multi-commodity flow problem. This research proposes a novel hybrid-link-based model that nests t...