Related papers: Structural Origins of Cubic Complexity in Pebble M…
Graph pebbling is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling…
Given a configuration of pebbles on the vertices of a connected graph $G$, a \emph{pebbling move} removes two pebbles from some vertex and places one pebble on an adjacent vertex. The \emph{pebbling number} of a graph $G$ is the smallest…
We consider an inverse problem for a finite graph $(X,E)$ where we are given a subset of vertices $B\subset X$ and the distances $d_{(X,E)}(b_1,b_2)$ of all vertices $b_1,b_2\in B$. The distance of points $x_1,x_2\in X$ is defined as the…
Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…
Consider a distribution of pebbles on a graph. A pebbling move removes two pebbles from a vertex and place one at an adjacent vertex. A vertex is reachable under a pebble distribution if it has a pebble after the application of a sequence…
Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: stack(G): the least integer t such that every…
Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This paper provides counterexamples to a monotonicity…
An $n$-vertex graph is degree 3-critical if it has $2n - 2$ edges and no proper induced subgraph with minimum degree at least 3. In 1988, Erd\H{o}s, Faudree, Gy\'arf\'as, and Schelp asked whether one can always find cycles of all short…
We study the problem of deterministically exploring an undirected and initially unknown graph with $n$ vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are…
We prove the first nontrivial worst-case lower bounds for two closely related problems. First, $\Omega(n^{3/2})$ degree-1 reductions, series-parallel reductions, and $\Delta$Y transformations are required in the worst case to reduce an…
Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles…
Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we…
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…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with $n$ self-crossings requires…
Graph pebbling is a network model for transporting discrete resources that are consumed in transit. Deciding whether a given configuration on a particular graph can reach a specified target is ${\sf NP}$-complete, even for diameter two…
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move one pebble is removed at vertices v and w adjacent…
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most…
A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. The pebbling number of a graph G is the minimum number pi(G) so that every configuration…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…