arXiv subjects

Evangelos Kranakis

Publications and source records attributed to Evangelos Kranakis.

At least 19 recordsLinked to original sources

arXiv2026

Search and Rescue on the Plane

We study a planar variant of the search and rescue problem whereby an agent starting at an arbitrary position $P_{θ,r} = (r\cosθ, r\sinθ)$ in the plane must locate an object at an unknown position on the positive $x$-axis and deliver it to the origin. Our main contribution is to characterize the optimal form of any competitive algorithm, derive closed-form expressions for the competitive ratio, and identify a critical angle $θ^* \approx 15.6^\circ$ which yields a phase transition to optimal competitive search and delivery in the following sense. For each angle $-π\leq θ\leq π$ we compute a checkpoint (landing position on the $x$-axis) where the agent must go first prior to initiating a search on the $x$-axis in order to optimize the competitive ratio of search and delivery. We show that if $|θ| \geq θ^*$ then the checkpoint is at the origin, while if $|θ| < θ^*$ then the agent should land at the checkpoint $(r \cdot k_{|θ|}, 0)$ on the $x$-axis, where $k_{|θ|}$ is a real number given by an explicit formula we present.

cs.DM↗

arXiv2026

Online Drone Coverage of Targets on a Line

We study a problem of online targets coverage by a drone or a sensor that is equipped with a camera or an antenna of fixed half-angle of view $α$. The targets to be monitored appear at arbitrary positions on a line barrier in an online manner. When a new target appears, the drone has to move to a location that covers the newly arrived target, as well as already existing targets. The objective is to design a coverage algorithm that optimizes the total length of the drone's trajectory. Our results are reported in terms of an algorithm's competitive ratio, i.e., the worst-case ratio (over all inputs) of its cost to that of an optimal offline algorithm. In terms of upper bounds, we present three online algorithms and prove bounds on their competitive ratios for every $α\in [0, π/2]$. The best of them, called \FA is significantly better than the other two for $π/6 < α< π/3$. In particular, for $α=π/4$, its worst case, \FA has competitive ratio $1.25$, while the other two have competitive ratio $\sqrt{2}$. Finally, we prove a lower bound on the competitive ratio of online algorithms for a drone with half-angle $α\in [0, π/4]$; this bound is a function of $α$ that achieves its maximum value at $α= π/4$ equal to $(1+\sqrt{2})/2 \approx 1.207$.

cs.DS↗

arXiv2025

Optimal and Heuristic Approaches for Platooning Systems with Deadlines

Efficient truck platooning is a key strategy for reducing freight costs, lowering fuel consumption, and mitigating emissions. Deadlines are critical in this context, as trucks must depart within specific time windows to meet delivery requirements and avoid penalties. In this paper, we investigate the optimal formation and dispatch of truck platoons at a highway station with finite capacity $L$ and deadline constraints $T$. The system operates in discrete time, with each arriving truck assigned a deadline of $T$ slot units. The objective is to leverage the efficiency gains from forming large platoons while accounting for waiting costs and deadline violations. We formulate the problem as a Markov decision process and analyze the structure of the optimal policy $π^\star$ for $L = 3$, extending insights to arbitrary $L$. We prove certain monotonicity properties of the optimal policy in the state space $\mathcal{S}$ and identify classes of unreachable states. Moreover, since the size of $\mathcal{S}$ grows exponentially with $L$ and $T$, we propose heuristics--including conditional and deep-learning based approaches--that exploit these structural insights while maintaining low computational complexity.

eess.SY↗

arXiv2025

Capturing a Moving Target by Two Robots in the F2F Model

We study a search problem on capturing a moving target on an infinite real line. Two autonomous mobile robots (which can move with a maximum speed of 1) are initially placed at the origin, while an oblivious moving target is initially placed at a distance $d$ away from the origin. The robots can move along the line in any direction, but the target is oblivious, cannot change direction, and moves either away from or toward the origin at a constant speed $v$. Our aim is to design efficient algorithms for the two robots to capture the target. The target is captured only when both robots are co-located with it. The robots communicate with each other only face-to-face (F2F), meaning they can exchange information only when co-located, while the target remains oblivious and has no communication capabilities. We design algorithms under various knowledge scenarios, which take into account the prior knowledge the robots have about the starting distance $d$, the direction of movement (either toward or away from the origin), and the speed $v$ of the target. As a measure of the efficiency of the algorithms, we use the competitive ratio, which is the ratio of the capture time of an algorithm with limited knowledge to the capture time in the full-knowledge model. In our analysis, we are mindful of the cost of changing direction of movement, and show how to accomplish the capture of the target with at most three direction changes (turns).

cs.RO↗

arXiv2025

Linear Search for Capturing an Oblivious Mobile Target in the Sender/Receiver Model

We consider linear search for capturing an oblivious moving target by two autonomous robots with different communicating abilities. Both robots can communicate Face-to-Face (F2F) when co-located but in addition one robot is a Sender (can also send messages wirelessly) and the other also a Receiver (can also receive messages wirelessly). This is known as Sender/Receiver (S/R, for short) communication model. The robots can move with max speed $1$. The moving target starts at distance $d$ from the origin and can move either with speed $v<1$ away from the origin in the ``away'' model or with speed $v \geq 0$ toward the origin in the ``toward'' model. We assume that the direction of motion of the target (i.e., whether it is the away or toward model) is known to the robots in advance. To capture the target the two robots must be co-located with it. We design new linear search algorithms and analyze the competitive ratio of the time required to capture the target. The approach takes into account various scenarios related to what the robots know about the search environment (e.g., starting distance or speed of the mobile, away or toward model, or a combination thereof). Our study contributes to understanding how asymmetric communication affects the competitive ratio of linear search.

cs.DC↗

arXiv2025

Optimal Task Offloading with Firm Deadlines for Mobile Edge Computing Systems

Under a dramatic increase in mobile data traffic, a promising solution for edge computing systems to maintain their local service is the task migration that may be implemented by means of Autonomous mobile agents (AMA). In designing an optimal scheme for task offloading to AMA, we define a system cost as a minimization objective function that comprises two parts. First, an offloading cost which can be interpreted as the cost of using computational resources from the AMA. Second, a penalty cost due to potential task expiration. To minimize the expected (timeaverage) cost over a given time horizon, we formulate a Dynamic programming (DP). However, the DP Equation suffers from the well-known curse of dimensionality, which makes computations intractable, especially for infinite system state space. To reduce the computational burden, we identify three important properties of the optimal policy and show that it suffices to evaluate the DP Equation on a finite subset of the state space only. We then prove that the optimal task offloading decision at a state can be inferred from that at its adjacent states, further reducing the computational load. We present simulations to verify the theoretical results and to provide insights into the considered system.

eess.SY↗

arXiv2025

Multimodal Search on a Line

Inspired by the diverse set of technologies used in underground object detection and imaging, we introduce a novel multimodal linear search problem whereby a single searcher starts at the origin and must find a target that can only be detected when the searcher moves through its location using the correct of $p$ possible search modes. The target's location, its distance $d$ from the origin, and the correct search mode are all initially unknown to the searcher. We prove tight upper and lower bounds on the competitive ratio for this problem. Specifically, we show that when $p$ is odd, the optimal competitive ratio is given by $2p+3+\sqrt{8(p+1)}$, whereas when $p$ is even, the optimal competitive ratio is given by $c$: the unique solution to $(c-1)^4-4p(c+1)^2(c-p-1)=0$ in the interval $\left[2p+1+\sqrt{8p},\infty\right)$. This solution $c$ has the explicit bounds $2p+3+\sqrt{8(p-1)}\leq c\leq 2p+3+\sqrt{8p}$. The optimal algorithms we propose require the searcher to move infinitesimal distances and change directions infinitely many times within finite intervals. To better suit practical applications, we also propose an approximation algorithm with a competitive ratio of $c+\varepsilon$ (where $c$ is the optimal competitive ratio and $\varepsilon > 0$ is an arbitrarily small constant). This algorithm involves the searcher moving finite distances and changing directions a finite number of times within any finite interval.

cs.DM↗

arXiv2024

Bike Assisted Evacuation on a Line of Robots with Communication Faults

Two autonomous mobile robots and a non-autonomous one, also called bike, are placed at the origin of an infinite line. The autonomous robots can travel with maximum speed $1$. When a robot rides the bike its speed increases to $v>1$, however only exactly one robot at a time can ride the bike and the bike is non-autonomous in that it cannot move on its own. An Exit is placed on the line at an unknown location and at distance $d$ from the origin. The robots have limited communication behavior; one robot is a sender (denoted by S) in that it can send information wirelessly at any distance and receive messages only in F2F (Face-to-Face), while the other robot is a receiver (denoted by R) in that it can receive information wirelessly but can send information only F2F. The bike has no communication capabilities of its own. We refer to the resulting communication model of the ensemble of the two autonomous robots and the bike as S/R. Our general goal is to understand the impact of the non-autonomous robot in assisting the evacuation of the two autonomous faulty robots. Our main contribution is to provide a new evacuation algorithm that enables both robots to evacuate from the unknown Exit in the S/R model. We also analyze the resulting evacuation time as a function of the bike's speed $v$ and give upper and lower bounds on the competitive ratio of the resulting algorithm for the entire range of possible values of $v$.

cs.DC↗

arXiv2024

Optimal Delivery with a Faulty Drone

We introduce and study a new cooperative delivery problem inspired by drone-assisted package delivery. We consider a scenario where a drone, en route to deliver a package to a destination (a point on the plane), unexpectedly loses communication with its central command station. The command station cannot know whether the drone's system has wholly malfunctioned or merely experienced a communications failure. Consequently, a second, helper drone must be deployed to retrieve the package to ensure successful delivery. The central question of this study is to find the optimal trajectory for this second drone. We demonstrate that the optimal solution relies heavily on the relative spatial positioning of the command station, the destination point, and the last known location of the disconnected drone.

cs.DM↗

arXiv2024

Linear Search for an Escaping Target with Unknown Speed

We consider linear search for an escaping target whose speed and initial position are unknown to the searcher. A searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed $1$ in either direction along the line. An oblivious mobile target that is moving away from the origin with an unknown constant speed $v<1$ is initially placed by an adversary on the infinite line at distance $d$ from the origin in an unknown direction. We consider two cases, depending on whether $d$ is known or unknown. The main contribution of this paper is to prove a new lower bound and give algorithms leading to new upper bounds for search in these settings. This results in an optimal (up to lower order terms in the exponent) competitive ratio in the case where $d$ is known and improved upper and lower bounds for the case where $d$ is unknown. Our results solve an open problem proposed in [Coleman et al., Proc. OPODIS 2022].

cs.DM↗

arXiv2023

Optimal Task Offloading Policy in Edge Computing Systems with Firm Deadlines

The recent drastic increase in mobile data traffic has pushed the mobile edge computing systems to the limit of their capacity. A promising solution to this problem is the task migration provided by unmanned aerial vehicles (UAV). Key factors to be taken into account in the design of UAV offloading schemes must include the number of tasks waiting in the system as well as their corresponding deadlines. An appropriate system cost which is used as an objective function to be minimized comprises two parts. First, an offloading cost which can be interpreted as the cost of using computational resources at the UAV. Second, a penalty cost due to potential task expiration. In order to minimize the expected (time average) cost over a time horizon, we formulate a Dynamic Programming (DP) equation and analyze it to describe properties of a candidate optimal offloading policy. The DP equation suffers from the well-known "Curse of Dimensionality" that makes computations intractable, especially when the state space is infinite. In order to reduce the computational burden, we identify three important properties of the optimal policy. Based on these properties, we show that it suffices to evaluate the DP equation on a finite subset of the state space only. We then show that the optimal task offloading decision associated with a state can be inferred from the decision taken at its "adjacent" states, further reducing the computational load. Finally, we provide numerical results to evaluate the influence of different parameters on the system performance as well as verify the theoretical results.

eess.SY↗

arXiv2023

Overcoming Probabilistic Faults in Disoriented Linear Search

We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all agents reach the target sooner or later. A special feature of our problem is that the agents are $p$-faulty, meaning that every attempt to change direction is an independent Bernoulli trial with known probability $p$, where $p$ is the probability that a turn fails. We are looking for agent trajectories that minimize the worst-case expected termination time, relative to competitive analysis. First, we study linear search with one deterministic $p$-faulty agent, i.e., with no access to random oracles, $p\in (0,1/2)$. For this problem, we provide trajectories that leverage the probabilistic faults into an algorithmic advantage. Our strongest result pertains to a search algorithm (deterministic, aside from the adversarial probabilistic faults) which, as $p\to 0$, has optimal performance $4.59112+ε$, up to the additive term $ε$ that can be arbitrarily small. Additionally, it has performance less than $9$ for $p\leq 0.390388$. When $p\to 1/2$, our algorithm has performance $Θ(1/(1-2p))$, which we also show is optimal up to a constant factor. Second, we consider linear search with two $p$-faulty agents, $p\in (0,1/2)$, for which we provide three algorithms of different advantages, all with a bounded competitive ratio even as $p\rightarrow 1/2$. Indeed, for this problem, we show how the agents can simulate the trajectory of any $0$-faulty agent (deterministic or randomized), independently of the underlying communication model. As a result, searching with two agents allows for a solution with a competitive ratio of $9+ε$, or a competitive ratio of $4.59112+ε$. Our final contribution is a novel algorithm for searching with two $p$-faulty agents that achieves a competitive ratio $3+4\sqrt{p(1-p)}$.

cs.DS↗

arXiv2023

Repeated Purification versus Concatenated Error Correction in Fault Tolerant Quantum Networks

Entanglement distribution is a core mechanism for the future quantum Internet. The quantum world is, however, a faulty environment. Hence, successful entanglement swapping is error-prone. The occurrence of quantum state errors can be mitigated using purification and error correction, which can be repeated in the former case and concatenated in the latter case. Repeated purification merges low-fidelity qubits into higher-quality ones, while concatenated error correction builds upon the redundancy of quantum information. In this article, we study in-depth and compare the two options: repeated purification and concatenated error correction. We consider using repeated purification and concatenated error correction to mitigate the presence of faults that occur during the establishment of Bell pairs between remote network nodes. We compare their performance versus the number of repetitions or concatenations, to reach a certain level of fidelity in quantum networks. We study their resource requirements, namely, their work memory complexity (e.g., number of stored qubits) and operational complexity (e.g., number of operations). Our analysis demonstrates that concatenated error correction, versus repeated purification, requires fewer iterations and has lower operational complexity than repeated purification to reach high fidelity at the expense of increased memory requirements.

quant-ph↗

arXiv2022

Optimal Control for Platooning in Vehicular Networks

As the automotive industry is developing autonomous driving systems and vehicular networks, attention to truck platooning has increased as a way to reduce costs (fuel consumption) and improve efficiency in the highway. Recent research in this area has focused mainly on the aerodynamics, network stability, and longitudinal control of platoons. However, the system aspects (e.g., platoon coordination) are still not well explored. In this paper, we formulate a platooning coordination problem and study whether trucks waiting at an initial location (station) should wait for a platoon to arrive in order to leave. Arrivals of trucks at the station and platoons by the station are modelled by independent Bernoulli distributions. Next we use the theory of Markov Decision Processes to formulate the dispatching control problem and derive the optimal policy governing the dispatching of trucks with platoons. We show that the policy that minimizes an average cost function at the station is of threshold type. Numerical results for the average cost case are presented. They are consistent with the optimal ones.

eess.SY↗

arXiv2022

Line Search for an Oblivious Moving Target

Consider search on an infinite line involving an autonomous robot starting at the origin of the line and an oblivious moving target at initial distance $d \geq 1$ from it. The robot can change direction and move anywhere on the line with constant maximum speed $1$ while the target is also moving on the line with constant speed $v>0$ but is unable to change its speed or direction. The goal is for the robot to catch up to the target in as little time as possible. The classic case where $v=0$ and the target's initial distance $d$ is unknown to the robot is the well-studied ``cow-path problem''. Alpert and Gal gave an optimal algorithm for the case where a target with unknown initial distance $d$ is moving away from the robot with a known speed $v<1$. In this paper we design and analyze search algorithms for the remaining possible knowledge situations, namely, when $d$ and $v$ are known, when $v$ is known but $d$ is unknown, when $d$ is known but $v$ is unknown, and when both $v$ and $d$ are unknown. Furthermore, for each of these knowledge models we consider separately the case where the target is moving away from the origin and the case where it is moving toward the origin. We design algorithms and analyze competitive ratios for all eight cases above. The resulting competitive ratios are shown to be optimal when the target is moving towards the origin as well as when $v$ is known and the target is moving away from the origin.

cs.DC↗

arXiv2022

Delivery to Safety with Two Cooperating Robots

Two cooperating, autonomous mobile robots with arbitrary nonzero max speeds are placed at arbitrary initial positions in the plane. A remotely detonated bomb is discovered at some source location and must be moved to a safe distance away from its initial location as quickly as possible. In the Bomb Squad problem, the robots cooperate by communicating face-to-face in order to pick up the bomb from the source and carry it away to the boundary of a disk centered at the source in the shortest possible time. The goal is to specify trajectories which define the robots' paths from start to finish and their meeting points which enable face-to-face collaboration by exchanging information and passing the bomb from robot to robot. We design algorithms reflecting the robots' knowledge about orientation and each other's speed and location. In the offline case, we design an optimal algorithm. For the limited knowledge cases, we provide online algorithms which consider robots' level of agreement on orientation as per OneAxis and NoAxis models, and knowledge of the boundary as per Visible, Discoverable, and Invisible. In all cases, we provide upper and lower bounds for the competitive ratios of the online problems.

cs.DC↗

arXiv2021

Group Evacuation on a Line by Agents with Different Communication Abilities

We consider evacuation of a group of $n \geq 2$ autonomous mobile agents (or robots) from an unknown exit on an infinite line. The agents are initially placed at the origin of the line and can move with any speed up to the maximum speed $1$ in any direction they wish and they all can communicate when they are co-located. However, the agents have different wireless communication abilities: while some are fully wireless and can send and receive messages at any distance, a subset of the agents are senders, they can only transmit messages wirelessly, and the rest are receivers, they can only receive messages wirelessly. The agents start at the same time and their communication abilities are known to each other from the start. Starting at the origin of the line, the goal of the agents is to collectively find a target/exit at an unknown location on the line while minimizing the evacuation time, defined as the time when the last agent reaches the target. We investigate the impact of such a mixed communication model on evacuation time on an infinite line for a group of cooperating agents. In particular, we provide evacuation algorithms and analyze the resulting competitive ratio ($CR$) of the evacuation time for such a group of agents. If the group has two agents of two different types, we give an optimal evacuation algorithm with competitive ratio $CR=3+2 \sqrt{2}$. If there is a single sender or fully wireless agent, and multiple receivers we prove that $CR \in [2+\sqrt{5},5]$, and if there are multiple senders and a single receiver or fully wireless agent, we show that $CR \in [3,5.681319]$. Any group consisting of only senders or only receivers requires competitive ratio 9, and any other combination of agents has competitive ratio 3.

cs.DS↗

arXiv2021

Message Delivery in the Plane by Robots with Different Speeds

We study a fundamental cooperative message-delivery problem on the plane. Assume $n$ robots which can move in any direction, are placed arbitrarily on the plane. Robots each have their own maximum speed and can communicate with each other face-to-face (i.e., when they are at the same location at the same time). There are also two designated points on the plane, $S$ (the source) and $D$ (the destination). The robots are required to transmit the message from the source to the destination as quickly as possible by face-to-face message passing. We consider both the offline setting where all information (the locations and maximum speeds of the robots) are known in advance and the online setting where each robot knows only its own position and speed along with the positions of $S$ and $D$. In the offline case, we discover an important connection between the problem for two-robot systems and the well-known Apollonius circle which we employ to design an optimal algorithm. We also propose a $\sqrt 2$ approximation algorithm for systems with any number of robots. In the online setting, we provide an algorithm with competitive ratio $\frac 17 \left( 5+ 4 \sqrt{2} \right)$ for two-robot systems and show that the same algorithm has a competitive ratio less than $2$ for systems with any number of robots. We also show these results are tight for the given algorithm. Finally, we give two lower bounds (employing different arguments) on the competitive ratio of any online algorithm, one of $1.0391$ and the other of $1.0405$.

cs.DC↗