Related papers: Min-Cost Flow Duality in Planar Networks
The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
The concept of Reload cost in a graph refers to the cost that occurs while traversing a vertex via two of its incident edges. This cost is uniquely determined by the colors of the two edges. This concept has various applications in…
In this paper, we present an improved algorithm for the maximum flow problem on general networks with $n$ vertices and $m$ arcs. We show how to solve the problem in $O(mn)$ time, when $m = O(n^{2-\epsilon})$, for some $0 <\epsilon \leq 1$.…
Routing, modulation and spectrum allocation in elastic optical networks is a problem aiming at increasing the capacity of the network. Many algorithms such as shortest path algorithm can be used as the routing section of this problem. The…
This paper addresses the scheduling problem of coflows in identical parallel networks, which is a well-known $NP$-hard problem. Coflow is a relatively new network abstraction used to characterize communication patterns in data centers. We…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
In this paper we show that every maximum minimum-cost flow over time problem has an optimal solution with a repeated structure if the given time horizon is large enough.
The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on.…
The Fixed-Charge Network Flow problem is a well-studied NP-hard problem that has the goal of finding a flow in a network where fixed edge costs are incurred, regardless of the amount of flow hosted by the edge. In this paper, we consider…
We examine the dynamic network flow problem under the assumption that the flow consists of discrete units. The dynamic network flow problem is commonly addressed in the context of developing evacuation plans, where the flow is typically…
This paper studies the problem of computing quasi-upward planar drawings of bimodal plane digraphs with minimum curve complexity, i.e., drawings such that the maximum number of bends per edge is minimized. We prove that every bimodal plane…
We consider some flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of $m$ machines and a set of $n$ jobs, and each job $j$ has a machine dependent processing time of $p_{ij}$ on machine $i$.…
Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost $\sum_ec(e)f^2(e)$, where f(e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We…
Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance.…
We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network…
We give an $O(n \log \log n)$ time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest $O(n\log^3 n)$ solution. Interestingly, while in…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on…