Related papers: Graph Traversal via Connected Mobile Agents
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
Given a directed graph $G = (V, E)$, the $k$-path partition problem is to find a minimum collection of vertex-disjoint directed paths each of order at most $k$ to cover all the vertices of $V$. The problem has various applications in…
We study some variants of the $k$-\textsc{Watchman Routes} problem, the cooperative version of the classic \textsc{Watchman Routes} problem in a simple polygon. The watchmen may be required to see the whole polygon, or some pre-determined…
A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…
Rotor walks are cellular automata that determine deterministic traversals of particles in a directed multigraph using simple local rules, yet they can generate complex behaviors. Furthermore, these trajectories exhibit statistical…
Motivated by real-world applications such as the allocation of public housing, we examine the problem of assigning a group of agents to vertices (e.g., spatial locations) of a network so that the diversity level is maximized. Specifically,…
In this paper we tackle the problem of routing multiple agents in a coordinated manner. This is a complex problem that has a wide range of applications in fleet management to achieve a common goal, such as mapping from a swarm of robots and…
Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the…
The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph $G$ and a spanning tree $T$ for it, and the goal is to augment $T$ with a minimum set of edges $Aug$ from $G$, such that $T \cup Aug$…
Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
In the Survivable Network Design Problem (SNDP), the input is an edge-weighted (di)graph $G$ and an integer $r_{uv}$ for every pair of vertices $u,v\in V(G)$. The objective is to construct a subgraph $H$ of minimum weight which contains…
We consider a variant of the path cover problem, namely, the $k$-fixed-endpoint path cover problem, or kPC for short, on interval graphs. Given a graph $G$ and a subset $\mathcal{T}$ of $k$ vertices of $V(G)$, a $k$-fixed-endpoint path…
In this paper, we consider the partial gathering problem of mobile agents in asynchronous unidirectional rings equipped with whiteboards on nodes. The partial gathering problem is a new generalization of the total gathering problem. The…
We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move.…
This paper studies a team coordination problem in a graph environment. Specifically, we incorporate "support" action which an agent can take to reduce the cost for its teammate to traverse some edges that have higher costs otherwise. Due to…
We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
Recent years, multi-hop reasoning has been widely studied for knowledge graph (KG) reasoning due to its efficacy and interpretability. However, previous multi-hop reasoning approaches are subject to two primary shortcomings. First, agents…