An upper boundary point for a demand vector is defined to be a system state vector for which the system capacity is equal to the demand vector, and an increase in its unsaturated components leads to at least one unit of increase in system capacity. System capacity of a singlecommodity stochastic-flow network is the maximum flow from the source node to the sink node of the network. Extending the...

The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernández & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equati...

This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side...

Statistical analysis of land-use change plays an important role in sustainable land management and has received increasing attention from scholars and administrative departments. However, the statistical process involving spatial overlay analysis remains difficult and needs improvement to deal with mass land-use data. In this paper, we introduce a spatio-temporal flow network model to reveal th...

An unsplittable flow in a multicommodity network is a flow that routes each commoidty on a single path. In this paper, we introduce the unsplittable flow problem and an open conjecture of Goemans, which states that given a fractional flow it is possible to construct an unsplittable flow that only overflows each edge by at most the maximum demand of a commodity. We provide an intuitive explanati...

This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We provide a different approach to these problems which yields faster and much simpler algorithms. Our approach also allows us to substitute shortest path computations for min-cost flow computations in computing maximum concurrent flow and min...

We consider the maximum integral tWo-Commodity flow problem in augmented planar graphs (i.e., with both source-sink edges added) and provide an o(IVI 2 1ogIVI) algorithm for that problem. Let G = (V, E) be a graph and w : E-t Z+ a weight function. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. Lomonosov gave a good cha...

This paper proposes a complete network capacity analysis framework for low-earth-orbit (LEO) mega-constellations, where estimation problem considering the link packet loss rate is formulated with support of time-variant topology model and task distribution model. solved in two steps. First, without rate, an improved fully polynomial-time approximation (IFPTA) algorithm proposed to provide sub-o...