Rendezvous of Heterogeneous Mobile Agents in Edge-Weighted Networks

Abstract

Abstract. We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal times for the other agent. The goal of the agents is to meet on an edge or a node of the graph. In this scenario, we study the time required by the agents to meet, compared to the meeting time TOPT in the offline scenario in which the agents have complete knowledge about each others speed characteristics. When no additional assumptions are made, we show that rendezvous in our model can be achieved after time O(nTOPT) in a n-node graph, and that such time is essentially in some cases the best possible. However, we prove that the rendezvous time can be reduced to Θ(TOPT) when the agents are allowed to exchange Θ(n) bits of information at the start of the rendezvous process. We then show that under some natural assumption about the traversal times of edges, the hardness of the heterogeneous rendezvous problem can be substantially decreased, both in terms of time required for rendezvous without communication, and the communication complexity of achieving rendezvous in time Θ(TOPT).

Agent-Based Simulators for Empowering Patients in Self-Care Programs Using Mobile Agents with Machine Learning

“…e remaining algorithm is deterministic and does not require unique identifiers, but its complexity has not proven to reach asymptotic optimality. Moreover, Dereniowski et al [12] introduced the rendezvous problem for two heterogeneous mobile agents in an undirected graph. ese are required to traverse certain edges at different times.…”

Searching by Heterogeneous Agents

“…We conclude by pointing to few works that use heterogeneous agents for solving different computational tasks, mostly in the area of mobile agent computing. These include modeling traffic flow [35], meeting [29] or rendezvous [17,19,20]. We also note that heterogeneity can be introduced by providing weights to mobile agents, where the meaning of the weight is specific to a particular problem to be solved [4,10,27], while in [11] authors consider patrolling by robots with distinct speeds and visibility ranges.…”

A New Complex Network Model with Multiweights and Its Synchronization Control

“…The proposed concept of weight successfully solved that problem, and then, weighted complex networks arisen. In the next few years, a lot of research works have fully demonstrate the feasibility and practicality of weighted complex networks [14][15][16][17][18][19]. For example, Wang et al [14] designed a novel edge-weight-based compartmental approach and proposed an edge-weight-based removal strategy, which can control the spread of epidemic effectively when the highly weighted edges are preferentially removed.…”