Related papers: I/O-optimal algorithms on grid graphs

The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…

We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast, linear-time…

We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…

This paper proposes earliest and latest path algorithms based on binary weight allocation, assigning weights of 2(i-1) and 2(m-i) to the i-th arc in a network. While traditional shortest path algorithms optimize only distance, our approach…

An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$…

We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…

This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…

The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…

A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…

In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…

We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…

We describe a simple variant of Hierholzer's algorithm that finds an Eulerian cycle in a (multi)graph with $n$ vertices and $m$ edges using $\mathrm{O}(n \lg m)$ bits of working memory. This substantially improves the working space compared…

We develop a time-optimal $O(mn^2)$-time algorithm to construct the subtree prune-regraft (SPR) graph on a collection of m phylogenetic trees with n leaves. This improves on the previous bound of $O(mn^3)$. Such graphs are used to better…

The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…

We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…

We prove crossing number inequalities for geometric graphs whose vertex sets are taken from a d-dimensional grid of volume N and give applications of these inequalities to counting the number of non-crossing geometric graphs that can be…

In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$…

Python implementation of selected weighted graph algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are…

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…