Related papers: A fast parallel algorithm for minimum-cost small i…
We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…
We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady…
We consider the problem of finding maximum flows in planar graphs with capacities on both vertices and edges and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in $O(n…
We consider flow rounding: finding an integral flow from a fractional flow. Costed flow rounding asks that we find an integral flow with no worse cost. Randomized flow rounding requires we randomly find an integral flow such that the…
We show that a simple algorithm for computing a matching on a graph runs in a logarithmic number of phases incurring work linear in the input size. The algorithm can be adapted to provide efficient algorithms in several models of…
We present formalisations of the correctness of executable algorithms to solve minimum-cost flow problems in Isabelle/HOL. Two of the algorithms are based on the technique of scaling, most notably Orlin's algorithm, which has the fastest…
In this paper, we develop an $O((m \log k) {\rm MSF} (n,m,1))$-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with $n$ nodes, $m$ edges, and $k$ terminals, where ${\rm MSF}…
The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. Kaplan, Shamir, and Tarjan [FOCS 1994] have shown that the problem is solvable in time O(2^(O(k)) + k2 * nm) on graphs with n vertices and m…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…
In the {\sc Min-Sum 2-Clustering} problem, we are given a graph and a parameter $k$, and the goal is to determine if there exists a 2-partition of the vertex set such that the total conflict number is at most $k$, where the conflict number…
This paper addresses the output-sensitive complexity for linear multi-objective integer minimum cost flow (MOIMCF) problems and provides insights about the time complexity for enumerating all supported nondominated vectors. The paper shows…
In this paper we show an O(n^(3/2) log^2 n) time algorithm for finding a maximum flow in a planar graph with multiple sources and multiple sinks. This is the fastest algorithm whose running time depends only on the number of vertices in the…
We present an $m^{4/3+o(1)}\log W$-time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where $W$ is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver…
We present the first $m\,\text{polylog}(n)$ work, $\text{polylog}(n)$ time algorithm in the PRAM model that computes $(1+\epsilon)$-approximate single-source shortest paths on weighted, undirected graphs. This improves upon the breakthrough…
In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the…
Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…
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…