Related papers: Connectome graphs and maximum flow problems
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of…
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
In this paper we consider the problem of optimizing the ecological connectivity of a landscape under a budget constraint by improving habitat areas and ecological corridors between them. We consider a formulation of this problem in terms of…
We study the maximum number of straight-line segments connecting $n$ points in convex position in the plane, so that each segment intersects at most $k$ others. This question can also be framed as the maximum number of edges of an outer…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in path-pairable planar graphs. We show that any $n$-vertex…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
We give an $O(n^{1.5}\log n)$ time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs.
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
For a graph G with real weights assigned to the vertices (edges), the MAX H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if one exists. The all-pairs MAX H-SUBGRAPH problem is to find for every pair of vertices…
The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…
In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice…
A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…