Related papers: To reorient is easier than to orient: an on-line a…
An orientation of a given static graph is called transitive if for any three vertices $a,b,c$, the presence of arcs $(a,b)$ and $(b,c)$ forces the presence of the arc $(a,c)$. If only the presence of an arc between $a$ and $c$ is required,…
Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…
The modular decomposition of a graph is a canonical representation of its modules. Algorithms for computing the modular decomposition of directed and undirected graphs differ significantly, with the undirected case being simpler, and…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
The orientation theorem of Nash-Williams states that an undirected graph admits a $k$-arc-connected orientation if and only if it is $2k$-edge-connected. Recently, Ito et al. showed that any orientation of an undirected $2k$-edge-connected…
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for…
A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
To reversify an arbitrary sequential algorithm $A$, we gently instrument $A$ with bookkeeping machinery. The result is a step-for-step reversible algorithm that mimics $A$ step-for-step and stops exactly when $A$ does. Without loss of…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
We modify the Pearce-Kelly algorithm that maintains a topological ordering for a directed acyclic graph in order to allow cycles to be tolerated. Cycles make topological orderings moot, of course, however tolerating them is useful in…
A classical theorem of Ghouila-Houri from 1960 asserts that every directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$ contains a directed Hamilton cycle. In this paper we extend this theorem to a random…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not…
Trajectory prediction for surrounding agents is a challenging task in autonomous driving due to its inherent uncertainty and underlying multimodality. Unlike prevailing data-driven methods that primarily rely on supervised learning, in this…