Who Let the Guards Out: Visual Support for Patrolling Games

TL;DR

This work tackles the challenge of designing and evaluating patrolling strategies represented as Markov-chain–based processes on graphs of patrolled sites. It introduces a visual analytics tool that combines a node graph, edge aggregation, transition matrices, and dynamic agent simulations to reveal stable paths, long-term visitation patterns, and potential anomalies. Three case studies illustrate the tool’s ability to detect unused memory nodes, track patrol trajectories, and assess overall strategy robustness, with a public prototype provided. Key contributions include design requirements, novel visualization techniques such as memory-node flower glyphs and an axial force layout, and demonstrated applicability to broader Markov-chain visualization tasks in networked systems.

Abstract

Effective security patrol management is critical for ensuring safety in diverse environments such as art galleries, airports, and factories. The behavior of patrols in these situations can be modeled by patrolling games. They simulate the behavior of the patrol and adversary in the building, which is modeled as a graph of interconnected nodes representing rooms. The designers of algorithms solving the game face the problem of analyzing complex graph layouts with temporal dependencies. Therefore, appropriate visual support is crucial for them to work effectively. In this paper, we present a novel tool that helps the designers of patrolling games explore the outcomes of the proposed algorithms and approaches, evaluate their success rate, and propose modifications that can improve their solutions. Our tool offers an intuitive and interactive interface, featuring a detailed exploration of patrol routes and probabilities of taking them, simulation of patrols, and other requested features. In close collaboration with experts in designing patrolling games, we conducted three case studies demonstrating the usage and usefulness of our tool. The prototype of the tool, along with exemplary datasets, is available at https://gitlab.fi.muni.cz/formela/strategy-vizualizer.

Figures (15)

• Figure 1: Node-link diagrams depicting Markov chains. (a) a typical example with probabilities as edge labels (self-loops are omitted) norris1998. (b) probabilities are displayed as the edge line weight bosansky2011.
• Figure 2: (a) Example of a plain Markov chain strategy. The probability of going from left to right without returning is 25 %. (b) In the expanded version, where the patrol retains memory, the probability is 100 %.
• Figure 3: Node-link diagrams laid out to resemble a map. (a) a three-floor hotel klaska2021. (b) a storage facility with six zones klaska2020.
• Figure 4: A line-graph-like approach zhang2019. Even with a small number of locations, the graph gets very cluttered and unreadable.
• Figure 5: (a) A representation of a building with each location marked by a different color. (b) The same building, with a strategy applied. Each location can be present multiple times as a memory node. Coding by colors is insufficient to track the behavior of the patrol.