Related papers: A Tight Max-Flow Min-Cut Duality Theorem for Non-L…
The max-k-cut problem is to partition the vertices of a weighted graph $G = (V,E)$ into $k\geq2$ disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut…
Computing routing schemes that support both high throughput and low latency is one of the core challenges of network optimization. Such routes can be formalized as $h$-length flows which are defined as flows whose flow paths are restricted…
Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem we are given a general weighted graph…
We introduce a new technique to certify lower bounds on the multicut size using network coding. In directed networks the network coding rate is not a lower bound on the multicut, but we identify a class of networks on which the rate is…
We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow through a…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…
We present a deterministic channel model which captures several key features of multiuser wireless communication. We consider a model for a wireless network with nodes connected by such deterministic channels, and present an exact…
In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
We consider single-sink network flow problems. An instance consists of a capacitated graph (directed or undirected), a sink node $t$ and a set of demands that we want to send to the sink. Here demand $i$ is located at a node $s_i$ and…
In this paper we describe a new algorithm for buffered global routing according to a prescribed buffer site map. Specifically, we describe a provably good multi-commodity flow based algorithm that finds a global routing minimizing buffer…
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…
We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
We consider the problem of reserving link capacity in a network in such a way that any of a given set of flow scenarios can be supported. In the optimal capacity reservation problem, we choose the reserved link capacities to minimize the…
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a…
We consider the problem of multi-path entanglement distribution to a pair of nodes in a quantum network consisting of devices with non-deterministic entanglement swapping capabilities. Multi-path entanglement distribution enables a network…