Related papers: Multicommodity Flows in Planar Graphs with Demands…
A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. In this paper we decompose the set of all 1-planar graphs into three classes $\mathcal C_0, \mathcal C_1$ and…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
We introduce a new approach to the maximum flow problem in undirected, capacitated graphs using $\alpha$-\emph{congestion-approximators}: easy-to-compute functions that approximate the congestion required to route single-commodity demands…
The three-way table problem is to decide if there exists an l x m x n table satisfying given line sums, and find a table if there is one. It is NP-complete already for l=3 and every bounded integer program can be isomorphically represented…
In this paper we consider a ``flow'' of nonparametric solutions of the volume constrained Plateau problem with respect to a convex planar curve. Existence and regularity is obtained from standard elliptic theory, and convexity results for…
The multi-commodity flow-cut gap is a fundamental parameter that affects the performance of several divide \& conquer algorithms, and has been extensively studied for various classes of undirected graphs. It has been shown by Linial, London…
We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-eps)-approximation schemes for various versions of the multicommodity flow problem. In particular, if eps is moderately…
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…
This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as…
In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon…
A connected graph G is 3-flow-critical if G does not have a nowhere-zero 3-flow, but every proper contraction of G does. We prove that every n-vertex 3-flow-critical graph other than K_2 and K_4 has at least 5n/3 edges. This bound is tight…
As an alternative to previously existing planar graph product structure theorems, we prove that every planar graph $G$ is a subgraph of the strong product of $K_2$, a path and a planar subgraph of a $4$-tree. As an application, we show that…
We introduce the concept of low-step multi-commodity flow emulators for any undirected, capacitated graph. At a high level, these emulators contain approximate multi-commodity flows whose paths contain a small number of edges, shattering…
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Paths problem, have been considered. Therefore, we investigate the…
In 1972, Tutte posed the $3$-Flow Conjecture: that all $4$-edge-connected graphs have a nowhere zero $3$-flow. This was extended by Jaeger et al.(1992) to allow vertices to have a prescribed, possibly non-zero difference (modulo $3$)…
In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few…
Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem -- the all-or-nothing multicommodity flow (ANF) problem -- in arbitrary directed graphs and in the…
Dujmovi\'c et al. [\emph{J.~ACM}~'20] recently proved that every planar graph is isomorphic to a subgraph of the strong product of a bounded treewidth graph and a path. Analogous results were obtained for graphs of bounded Euler genus or…
A long-standing Conjecture of S. Negami states that a connected graph has a finite planar cover if and only if it embeds in the projective plane. It is known that the Conjecture is equivalent to the fact that \emph{the graph $K_{1,2, 2, 2}$…
In 1972, Tutte posed the $3$-Flow Conjecture: that all $4$-edge-connected graphs have a nowhere zero $3$-flow. This was extended by Jaeger et al.(1992) to allow vertices to have a prescribed, possibly non-zero difference (modulo $3$)…