Related papers: Comparing Pedigree Graphs
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
Funnels are a new natural subclass of DAGs. Intuitively, a DAG is a funnel if every source-sink path can be uniquely identified by one of its arcs. Funnels are an analog to trees for directed graphs that is more restrictive than DAGs but…
A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
We introduce a new algorithm called {\sc Rec-Gen} for reconstructing the genealogy or \textit{pedigree} of an extant population purely from its genetic data. We justify our approach by giving a mathematical proof of the effectiveness of…
Given a set of attributed subgraphs known to be from different classes, how can we discover their differences? There are many cases where collections of subgraphs may be contrasted against each other. For example, they may be assigned…
The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two…
Subgraph similarity search, one of the core problems in graph search, concerns whether a target graph approximately contains a query graph. The problem is recently touched by neural methods. However, current neural methods do not consider…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
In recent years there has been a rapid increase in classification methods on graph structured data. Both in graph kernels and graph neural networks, one of the implicit assumptions of successful state-of-the-art models was that…
The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an…
This paper presents a new graph isomorphism invariant, called $\mathfrak{w}$-labeling, that can be used to design a polynomial-time algorithm for solving the graph isomorphism problem for various graph classes. For example, all…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…
Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate…
Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes whose graphs (1-skeletons) contain the TSP polytope graphs as spanning subgraphs. While deciding adjacency of vertices in TSP polytopes is…
Phylogenetic comparative methods (PCMs) are widely used to study trait evolution. However, many evolutionary histories involve reticulate evolutionary scenarios, such as hybridization, that violate core assumptions of these methods. In this…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…