Related papers: Multiple-source multiple-sink maximum flow in plan…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
We present an alternative and simpler method for computing principal typings of flow networks. When limited to planar flow networks, the method can be made to run in fixed-parameter linear-time -- where the parameter not to be exceeded is…
Given an $n$-vertex planar directed graph with real edge lengths and with no negative cycles, we show how to compute single-source shortest path distances in the graph in $O(n\log^2n/\log\log n)$ time with O(n) space. This is an improvement…
This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…
In this paper we present an $\tilde{O}(m\sqrt{n}\log^{O(1)}U)$ time algorithm for solving the maximum flow problem on directed graphs with $m$ edges, $n$ vertices, and capacity ratio $U$. This improves upon the previous fastest running time…
We present a deterministic O(n log log n) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC'11 by a factor of log n. This…
We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multi-variate polynomials over a finite field of characteristic two for non-identity with zero.…
The support of a flow $x$ in a network is the subdigraph induced by the arcs $uv$ for which $x(uv)>0$. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of…
We prove that the single-source shortest-path problem on disk graphs can be solved in $O(n\log n)$ time, and that it can be solved on intersection graphs of fat triangles in $O(n\log^2 n)$ time.
We pull together previously established graph-theoretical results to produce the algorithm in the paper's title. The glue are three easy elementary lemmas.
A multiflow in a planar graph is uncrossed if its support paths do not cross. Recently such flows have played a role in approximation algorithms for maximum disjoint paths in "fully-planar" instances, where the combined supply-demand graph…
In 1961, Gomory and Hu showed that the All-Pairs Max-Flow problem of computing the max-flow between all $n\choose 2$ pairs of vertices in an undirected graph can be solved using only $n-1$ calls to any (single-pair) max-flow algorithm. Even…
We present faster high-accuracy algorithms for computing $\ell_p$-norm minimizing flows. On a graph with $m$ edges, our algorithm can compute a $(1+1/\text{poly}(m))$-approximate unweighted $\ell_p$-norm minimizing flow with…
In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k > 0 and some unknown circulation \psi on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow…
We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the…
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 give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…
We give an algorithm to route a multicommodity flow in a planar graph $G$ with congestion $O(\log k)$, where $k$ is the maximum number of terminals on the boundary of a face, when each demand edge lie on a face of $G$. We also show that our…
The maximum capacity path problem is to find a path from a source to a sink which has the maximum capacity among all paths. This paper addresses an extension of this problem which considers loss factors. It is called the generalized maximum…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…