Related papers: Graph Compact Orthogonal Layout Algorithm
In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
Knitting, an ancient fiber art, creates a structured fabric consisting of loops or stitches. Publishing hand knitting patterns involves lengthy testing periods and numerous knitters. Modeling knitting patterns with graphs can help expedite…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
Consider the following 2-respecting min-cut problem. Given a weighted graph $G$ and its spanning tree $T$, find the minimum cut among the cuts that contain at most two edges in $T$. This problem is an important subroutine in Karger's…
The problem of orienting the edges of an undirected graph such that the resulting digraph is acyclic and has a single source s and a single sink t has a long tradition in graph theory and is central to many graph drawing algorithms. Such an…
We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…
In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like…
We present algorithms that extend the path-based hierarchical drawing framework and give experimental results. Our algorithms run in $O(km)$ time, where $k$ is the number of paths and $m$ is the number of edges of the graph, and provide…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
Min orderings give a vertex ordering characterization, common to some graphs and digraphs such as interval graphs, complements of threshold tolerance graphs (known as co-TT graphs), and two-directional orthogonal ray graphs. An adjusted…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both…
The construction of large-scale, low-latency networks becomes difficult as the number of nodes increases. In general, the way to construct a theoretically optimal solution is unknown. However, it is known that some methods can construct…
We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…