Smart random walkers: the cost of knowing the path

TL;DR

This paper investigates how entropy-based information influences the efficiency of navigating networks with random walkers, revealing that minimal penalization significantly reduces walk length and depends on network topology.

Contribution

Introduces a penalization scheme for random walkers that balances randomness and bias, optimizing network navigation based on topology.

Findings

Small penalization greatly reduces walk length

Network topology influences optimal penalization

Restricted information enables efficient navigation

Abstract

In this work we study the problem of targeting signals in networks using entropy information measurements to quantify the cost of targeting. We introduce a penalization rule that imposes a restriction to the long paths and therefore focus the signal to the target. By this scheme we go continuously from fully random walkers to walkers biased to the target. We found that the optimal degree of penalization is mainly determined by the topology of the network. By analyzing several examples, we have found that a small amount of penalization reduces considerably the typical walk length, and from this we conclude that a network can be efficiently navigated with restricted information.