相关论文: Congestion in planar graphs with demands on faces

Let $G = (VG, AG)$ be a directed graph with a set $S \subseteq VG$ of terminals and nonnegative integer arc capacities $c$. A feasible multiflow is a nonnegative real function $F(P)$ of "flows" on paths $P$ connecting distinct terminals…

In this paper, we aim to mitigate congestion in traffic management systems by guiding travelers along system-optimal (SO) routes. However, we recognize that most theoretical approaches assume perfect driver compliance, which often does not…

Ride-sharing can reduce traffic congestion and thus reduce gas emissions and save travel time. However, transportation system with ride-sharing is currently inefficient due to low occupancy rate, high travel demand and some other factors.…

Coordinating the motion of multiple agents in constrained environments is a fundamental challenge in robotics, motion planning, and scheduling. A motivating example involves $n$ robotic arms, each represented as a line segment. The…

Millions of flows are routed concurrently through a modern data-center. These networks are often built as Clos topologies, and flow demands are constrained only by the link capacities at the ingress and egress points. The minimum congestion…

We consider a given region $\Omega$ where the traffic flows according to two regimes: in a region $C$ we have a low congestion, where in the remaining part $\Omega\setminus C$ the congestion is higher. The two congestion functions $H_1$ and…

Given a set $P$ of $n$ points in the plane, the unit-disk graph $G(P)$ is a graph with $P$ as its vertex set such that two points of $P$ have an edge if their Euclidean distance is at most $1$. We consider the problem of computing a maximum…

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…

To investigate the topological structure of Morse flows on the 2-disk we use the planar graphs as destinguished graph of the flow. We assume, that the flow is transversal to the boundary of the 2-disk. We give a list of all planar graph…

We propose to study maximum flow problems for connectome graphs. We suggest a few computational problems: finding vertex pairs with maximal flow, finding new edges which would increase the maximal flow. Initial computation results for some…

A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…

The page number of a directed acyclic graph $G$ is the minimum $k$ for which there is a topological ordering of $G$ and a $k$-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the…

In the classical Node-Disjoint Paths (NDP) problem, the input consists of an undirected $n$-vertex graph $G$, and a collection $\mathcal{M}=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand,…

Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…

This paper studies an important rate allocation problem that arises in many networked and distributed systems: steady-state traffic rate allocation from multiple sources to multiple service nodes when both (i) the access-path delay on each…

Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…

We give a density condition for when, subject to a necessary parity condition, an eulerian graph or digraph may be cellularly embedded in an orientable surface so that it has exactly two faces, each bounded by an euler circuit, one of which…

An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich…

An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…

We study the impact of forbidding short cycles to the edge density of $k$-planar graphs; a $k$-planar graph is one that can be drawn in the plane with at most $k$ crossings per edge. Specifically, we consider three settings, according to…