Related papers: Ordering Metro Lines by Block Crossings
Drawing graphs with the minimum number of crossings is a classical problem that has been studied extensively. Many restricted versions of the problem have been considered. For example, bipartite graphs can be drawn such that the two sets in…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…
Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…
Finding communities in graphs is one of the most well-studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single…
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…
We consider an optimization problem posed by an actual newspaper company, which consists of computing a minimum length route for a delivery truck, such that the driver only stops at street crossings, each time delivering copies to all…
Tanglegrams are drawings of two rooted binary phylogenetic trees and a matching between their leaf sets. The trees are drawn crossing-free on opposite sides with their leaf sets facing each other on two vertical lines. Instead of minimizing…
For all line-based transit systems like bus, metro and tram, the routes of the lines and the frequencies at which they are operated are determining for the operational performance of the system. However, as transit line planning happens…
We consider the classical Minimum Crossing Number problem: given an $n$-vertex graph $G$, compute a drawing of $G$ in the plane, while minimizing the number of crossings between the images of its edges. This is a fundamental and extensively…
The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
Street intersection counts and densities are ubiquitous measures in transport geography and planning. However, typical street network data and typical street network analysis tools can substantially overcount them. This article explains the…
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively.…
Problem definition: To mitigate excessive crowding in public transit networks, network expansion is often not feasible due to financial and time constraints. Instead, operators are required to make use of existing infrastructure more…