Related papers: Physically-motivated dynamical algorithms for the …
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…
This paper deals with the problem of finding, for a given graph and a given natural number k, a subgraph of k nodes with a maximum number of edges. This problem is known as the k-cluster problem and it is NP-hard on general graphs as well…
We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs $G$ and $H$, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list…
In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that…
We present an algorithm for determining whether a bipartite graph $G$ is 2-chordal (formerly doubly chordal bipartite). At its core this algorithm is an extension of the existing efficient algorithm for determining whether a graph is…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if…
Circular-arc graphs are intersection graphs of arcs on the circle. The aim of our work is to present a polynomial time algorithm testing whether two circular-arc graphs are isomorphic. To accomplish our task we construct decomposition…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…