Related papers: A general lower bound for collaborative tree explo…

In the Multiagent Path Finding problem (MAPF for short), we focus on efficiently finding non-colliding paths for a set of $k$ agents on a given graph $G$, where each agent seeks a path from its source vertex to a target. An important…

Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search…

We consider the problem of exploring an anonymous unoriented ring of size $n$ by $k$ identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based…

We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…

We consider the following generalization of the classic Binary Search Problem: a searcher is required to find a hidden target vertex $x$ in a graph $G$, by iteratively performing queries about vertices. A query to $v$ incurs a cost $c(v,…

Due to some significantly contradicting research results, we reconsider the problem of the online exploration of a simple grid cell environment. In this model an agent attains local information about the direct four-neigbourship of a…

We consider lower bounds on the number of spanning trees of connected graphs with degree bounded by $d$. The question is of interest because such bounds may improve the analysis of the improvement produced by memorisation in the runtime of…

Chung and Graham [J. London Math. Soc., 1983] claimed that there exists an $n$-vertex graph $G$ containing all $n$-vertex trees as subgraphs that has at most $\frac{5}{2}n \log_2 n + O(n)$ edges. We identify an error in their proof. This…

The Temporal Graph Exploration problem (TEXP) takes as input a temporal graph, i.e., a sequence of graphs $(G_i)_{i\in \mathbb{N}}$ on the same vertex set, and asks for a walk of shortest length visiting all vertices, where the $i$-th step…

In this paper, we study collision-free graph exploration in an anonymous pot labeled network. Two identical mobile agents, starting from different nodes in $G$ have to explore the nodes of $G$ in such a way that for every node $v$ in $G$,…

For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…

For a graph $G=(V,E)$ and a set $S\subseteq V(G)$ of size at least $2$, an $S$-Steiner tree $T$ is a subgraph of $G$ that is a tree with $S\subseteq V(T)$. Two $S$-Steiner trees $T$ and $T'$ are internally disjoint (resp. edge-disjoint) if…

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…

We consider a natural notion of search trees on graphs, which we show is ubiquitous in various areas of discrete mathematics and computer science. Search trees on graphs can be modified by local operations called rotations, which generalize…

In a 1989 paper titled "shortest paths without a map", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed…

We consider a set of agents who are attempting to iteratively learn the 'state of the world' from their neighbors in a social network. Each agent initially receives a noisy observation of the true state of the world. The agents then…

Consider the scenario where multiple agents have to move in an optimal way through a network, each one towards their ending position while avoiding collisions. By optimal, we mean as fast as possible, which is evaluated by a measure known…

Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…

Given a connected graph on whose edges we can build roads to connect the nodes, a number of agents hold possibly different perspectives on which edges should be selected by assigning different edge weights. Our task is to build a minimum…

We concentrate on some recent results of Egawa and Ozeki [J. Graph Theory, 2015 and Combinatorica, 2014], and He et al. [J. Graph Theory, 2002]. We give shorter proofs and polynomial time algorithms as well. We present two new proofs for…