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For a given labelled transition system (LTS), synthesis is the task to find an unlabelled Petri net with an isomorphic reachability graph. Even when just demanding an embedding into a reachability graph instead of an isomorphism, a solution…
While a natural fit for modeling and understanding mobile networks, time-varying graphs remain poorly understood. Indeed, many of the usual concepts of static graphs have no obvious counterpart in time-varying ones. In this paper, we…
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk?…
A good edge-labelling of a simple graph is a labelling of its edges with real numbers such that, for any ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. Say a graph is good if it admits a good…
The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph $G$, we examine the problem of assigning directions to each edge of $G$…
A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time "11 a.m." and duration "7…
Let $G=(V,E)$ be an undirected graph with $n$ vertices and $m$ edges. We obtain the following new routing schemes: - A routing scheme for unweighted graphs that uses $\tilde O(\frac{1}{\epsilon} n^{2/3})$ space at each vertex and $\tilde…
The problem of characterizing testable graph properties (properties that can be tested with a number of queries independent of the input size) is a fundamental problem in the area of property testing. While there has been some extensive…
A graph is $k$-clique-extendible if there is an ordering of the vertices such that whenever two $k$-sized overlapping cliques $A$ and $B$ have $k-1$ common vertices, and these common vertices appear between the two vertices $a,b\in…
We prove that if an $n$-vertex graph $G$ can be drawn in the plane such that each pair of crossing edges is independent and there is a crossing-free edge that connects their endpoints, then $G$ has $O(n)$ edges. Graphs that admit such…
A graph whose edges only appear at certain points in time is called a temporal graph (among other names). Such a graph is temporally connected if each ordered pair of vertices is connected by a path which traverses edges in chronological…
The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the graph, then the vertices are allowed to check their…
A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…
A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. We show that optimal 1-planar graphs can be recognized in linear time. Our…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…
The diameter of a graph is one if its most important parameters, being used in many real-word applications. In particular, the diameter dictates how fast information can spread throughout data and communication networks. Thus, it is a…