Related papers: A Row-wise Algorithm for Graph Realization
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial…
Given a directed graph $D=(V,A)$ with a set of $d$ specified vertices $S=\{s_1,...,s_d\}\subseteq V$ and a function $f\colon S \to \mathbb{Z}_+$ where $\mathbb{Z}_+$ denotes the set of non-negative integers, we consider the problem which…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of…
A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
In this paper, we investigate the problem of generating the spanning trees of a graph $G$ up to the automorphisms or "symmetries" of $G$. After introducing and surveying this problem for general input graphs, we present algorithms that…
The problem of finding a spanning forest of a graph in a distributed-processing environment is studied. If an input graph is weighted, then the goal is to find a minimum-weight spanning forest. The processors communicate by broadcasting.…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
A graph $H$ is an induced subgraph of a graph $G$ if a graph isomorphic to $H$ can be obtained from $G$ by deleting vertices. Recently, there has been significant interest in understanding the unavoidable induced subgraphs for graphs of…
The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In…
With the current burst of network theory (especially in connection with social and biological networks) there is a renewed interest on realizations of given degree sequences. In this paper we propose an essentially new degree sequence…
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…
We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…