arXiv subjects

Euripides Markou

Publications and source records attributed to Euripides Markou.

5 recordsLinked to original sources

arXiv2025

Finite Pinwheel Scheduling: the k-Visits Problem

Pinwheel Scheduling is a fundamental scheduling problem, in which each task $i$ is associated with a positive integer $d_i$, and the objective is to schedule one task per time slot, ensuring each task perpetually appears at least once in every $d_i$ time slots. Although conjectured to be PSPACE-complete, the complexity of Pinwheel Scheduling remains open. We introduce k-Visits, a finite version of Pinwheel Scheduling, where given n deadlines, the goal is to schedule each task exactly k times. While we observe that the 1-Visit problem is trivial, we prove that 2-Visits is strongly NP-complete through a surprising reduction from Numerical 3-Dimensional Matching (N3DM). As intermediate steps in the reduction, we define NP-complete variants of N3DM which may be of independent interest. We further extend our strong NP-hardness result to a generalization of k-Visits $k\geq 2$ in which the deadline of each task may vary throughout the schedule, as well as to a similar generalization of Pinwheel Scheduling, thus making progress towards settling the complexity of Pinwheel Scheduling. Additionally, we prove that 2-Visits can be solved in linear time if all deadlines are distinct, rendering it one of the rare natural problems which exhibit the interesting dichotomy of being in P if their input is a set and NP-complete if the input is a multiset. We achieve this through a Turing reduction from 2-Visits to a variation of N3DM, which we call Position Matching. Based on this reduction, we also show an FPT algorithm for 2-Visits parameterized by a value related to how close the input deadlines are to each other, as well as a linear-time algorithm for instances with up to two distinct deadlines.

cs.DS↗

arXiv2017

Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each node of the graph is visited before its deadline by a reliable robot. The edge weight corresponds to the time needed by a robot to traverse the edge. Given the number of robots which may crash, is it possible to design an algorithm, which will always guarantee the exploration, independently of the choice of the subset of unreliable robots by the adversary? We find the optimal time, during which the graph may be explored. Our approach permits to find the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored. We concentrate on line graphs and rings, for which we give positive results. We start with the case of the collections involving only reliable robots. We give algorithms finding optimal times needed for exploration when the robots are assigned to fixed initial positions as well as when such starting positions may be determined by the algorithm. We extend our consideration to the case when some number of robots may be unreliable. Our most surprising result is that solving the line exploration problem with robots at given positions, which may involve crash-faulty ones, is NP-hard. The same problem has polynomial solutions for a ring and for the case when the initial robots' positions on the line are arbitrary. The exploration problem is shown to be NP-hard for star graphs, even when the team consists of only two reliable robots.

cs.DS↗

arXiv2016

Mobile Agents Rendezvous in spite of a Malicious Agent

We examine the problem of rendezvous, i.e., having multiple mobile agents gather in a single node of the network. Unlike previous studies, we need to achieve rendezvous in presence of a very powerful adversary, a malicious agent that moves through the network and tries to block the honest agents and prevents them from gathering. The malicious agent is assumed to be arbitrarily fast, has full knowledge of the network and it cannot be exterminated by the honest agents. On the other hand, the honest agents are assumed to be quite weak: They are asynchronous and anonymous, they have only finite memory, they have no prior knowledge of the network and they can communicate with the other agents only when they meet at a node. Can the honest agents achieve rendezvous starting from an arbitrary configuration in spite of the malicious agent? We present some necessary conditions for solving rendezvous in spite of the malicious agent in arbitrary networks. We then focus on the ring and mesh topologies and provide algorithms to solve rendezvous. For ring networks, our algorithms solve rendezvous in all feasible instances of the problem, while we show that rendezvous is impossible for an even number of agents in unoriented rings. For the oriented mesh networks, we prove that the problem can be solved when the honest agents initially form a connected configuration without holes if and only if they can see which are the occupied nodes within a two-hops distance. To the best of our knowledge, this is the first attempt to study such a powerful and mobile fault model, in the context of mobile agents. Our model lies between the more powerful but static fault model of black holes (which can even destroy the agents), and the less powerful but mobile fault model of Byzantine agents (which can only imitate the honest agents but can neither harm nor stop them).

cs.DC↗

arXiv2011

Black Hole Search with Finite Automata Scattered in a Synchronous Torus

We consider the problem of locating a black hole in synchronous anonymous networks using finite state agents. A black hole is a harmful node in the network that destroys any agent visiting that node without leaving any trace. The objective is to locate the black hole without destroying too many agents. This is difficult to achieve when the agents are initially scattered in the network and are unaware of the location of each other. Previous studies for black hole search used more powerful models where the agents had non-constant memory, were labelled with distinct identifiers and could either write messages on the nodes of the network or mark the edges of the network. In contrast, we solve the problem using a small team of finite-state agents each carrying a constant number of identical tokens that could be placed on the nodes of the network. Thus, all resources used in our algorithms are independent of the network size. We restrict our attention to oriented torus networks and first show that no finite team of finite state agents can solve the problem in such networks, when the tokens are not movable. In case the agents are equipped with movable tokens, we determine lower bounds on the number of agents and tokens required for solving the problem in torus networks of arbitrary size. Further, we present a deterministic solution to the black hole search problem for oriented torus networks, using the minimum number of agents and tokens.

cs.DS↗

arXiv2011

Tight Bounds for Black Hole Search with Scattered Agents in Synchronous Rings

We study the problem of locating a particularly dangerous node, the so-called black hole in a synchronous anonymous ring network with mobile agents. A black hole is a harmful stationary process residing in a node of the network and destroying destroys all mobile agents visiting that node without leaving any trace. We consider the more challenging scenario when the agents are identical and initially scattered within the network. Moreover, we solve the problem with agents that have constant-sized memory and carry a constant number of identical tokens, which can be placed at nodes of the network. In contrast, the only known solutions for the case of scattered agents searching for a black hole, use stronger models where the agents have non-constant memory, can write messages in whiteboards located at nodes or are allowed to mark both the edges and nodes of the network with tokens. This paper solves the problem for ring networks containing a single black hole. We are interested in the minimum resources (number of agents and tokens) necessary for locating all links incident to the black hole. We present deterministic algorithms for ring topologies and provide matching lower and upper bounds for the number of agents and the number of tokens required for deterministic solutions to the black hole search problem, in oriented or unoriented rings, using movable or unmovable tokens.

cs.MA↗