We present a comprehensive analysis of Round-Asynchronous Amnesiac Flooding (RAAF), a variant of Amnesiac Flooding that introduces round-based asynchrony through adversarial delays. We establish fundamental properties of RAAF, including termination characteristics for different graph types and decidability results under various adversarial models. Our key contributions include: (1) a formal model of RAAF incorporating round-based asynchrony, (2) a proof that flooding always terminates on acyclic graphs despite adversarial delays, (3) a construction showing non-termination is possible on any cyclic graph, (4) a demonstration that termination is undecidable with arbitrary computable adversaries, and (5) the introduction of Eventually Periodic Adversaries (EPA) under which termination becomes decidable. These results enhance our understanding of flooding processes in asynchronous settings and provide insights for designing robust distributed protocols.
Unmanned Aerial Vehicles (UAVs) are increasingly used in critical infrastructure maintenance due to their ability to improve safety, efficiency, and access in challenging environments. This paper focuses on optimizing drone-assisted equipment delivery for high-voltage power line maintenance, with the goal of minimizing the number of drones required to serve all pylons that lie on a line. Unlike prior work that maximizes delivery profit given a fixed fleet size, we aim to minimize the fleet size itself, addressing deployment constraints, such as load and energy, and coordination complexity. We introduce a new optimization problem, the Minimum Drone Delivery Problem (MDDP), and study three key variants: unitary loads (MDDP-U), arbitrary loads (MDDP-A), and non-overlapping missions (N-MDDP). We formulate MDDP as an Integer Linear Program and prove its NP -hardness. To solve it, we propose polynomial-time approximation algorithms and a heuristic. Extensive evaluations on synthetic datasets demonstrate the effectiveness and scalability of our approaches.
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the vertex-selection problem at each time such that we can reconfigure from one solution to the next. We can think of each solution in the sequence as a set of vertices with tokens placed on them; our reconfiguration model allows us to slide tokens along active edges of a temporal graph at each time-step. We show that it is possible to efficiently check whether one solution can be reconfigured to another, and show that approximation results on the static vertex-selection problem can be adapted with a lifetime factor to the reconfiguration version. Our main contributions are fixed-parameter tractable algorithms with respect to: enumeration time of the related static problem; the combination of temporal neighbourhood diversity and lifetime of the input temporal graph; and the combination of lifetime and treewidth of the footprint graph.
We investigate the trade-offs between size and query time that are attainable by fastest-path oracles for temporal trees, i.e., data structures capable of reporting the duration of a fastest point-to-point temporal path, possibly constrained to be within a given time window. For any parameter t ≥ 1 of choice, we provide an oracle of size O(M + M^2/t^2) answering queries in time O(t log (1+L) ) , where L is the maximum number of time-labels of a single edge, and M is the overall number of (not necessarily distinct) time-labels. We also prove a conditional lower bound that relies on the difficulty of the Set Disjointness problem, showing that the trade-offs obtained by our oracles are tight, up to polylogarithmic factors. We also investigate the case of general temporal graphs and we provide some evidences that the problem becomes much more challenging even for the special case of temporal reachability queries with no time constraints.
We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously known solution for capturing a robber in the zero-visibility case is based on the pathwidth decomposition. We provide an alternative solution based on a separation hierarchy, improving capture time and space complexity without asymptotically increasing the zero-visibility cop number in most cases. In addition, we provide a better bound on the approximate zero-visibility cop number for various classes of graphs, where approximate refers to the restriction to polynomial time computable strategies.
