arXiv subjects

Konstantinos Georgiou

Publications and source records attributed to Konstantinos Georgiou.

At least 19 recordsLinked to original sources

arXiv2026

Oblivious Self-Distance Symmetric Rendezvous on the Integer Line

Symmetric rendezvous on the line is a search problem in which two agents, initially placed at distance $2d$, must follow the same randomized strategy to meet as quickly as possible. In the standard model, agents may condition their actions on the entire execution history, and both the known- and unknown-distance variants admit expected rendezvous time $Θ(d)$. We study the role of memory by introducing oblivious self-distance strategies, in which an agent's decision depends only on her position relative to her own starting location. For an initial separation of $2d$, let $R_d$ denote the optimal oblivious expected rendezvous time in the known-distance setting. We develop two finite-state frameworks based on absorbing Markov chains. Truncated chains give computable upper bounds through finite-support strategies, while weak-peek chains give lower bounds through a revealed-information relaxation. Together, they provide a mechanism for certifying optimality. Using that mechanism, we determine $R_1$ exactly and prove that it is attained by a finite-support strategy. For $d=2,\ldots,6$, numerical optimization gives the same truncation structure and objective values, yielding rigorous upper bounds below $7.83d^2$. We do not prove that the computed weak-peek minimizers are global, but the stability of the computations leads us to conjecture that they are, in which case the corresponding truncated strategies are optimal. We also prove that $R_d=Θ(d^2)$. In the unknown-distance setting, we construct a universal strategy, independent of $d$, with expected rendezvous time $O(d^{2+η})$ for every fixed $η>0$. Thus, under the memory restriction, the known-distance rendezvous time becomes quadratic, while near-quadratic performance remains possible even without knowing $d$. The asymptotic analysis uses birth-death Markov chains and their electrical-network interpretation.

cs.DM↗

arXiv2026

ExPLoRe: Expert Patch-Level Loss Routing for Multi-Objective Masked Image Modeling

Multi-objective masked image modeling (MIM) combines complementary learning signals (token distillation, CLS alignment, and pixel reconstruction) but existing methods weight these objectives with global scalars, ignoring spatial heterogeneity across patches. We present ExPLoRe (Expert Patch-Level Loss Routing), which repurposes Soft Mixture of Experts (MoE) dispatch weights as learned, per-patch loss coefficients. The key mechanism is loss-coupling: allowing loss gradients to flow through dispatch weights to the router enables content-dependent specialization, where different patches receive different emphases across objectives. A detach ablation confirms loss-coupling as the core mechanism, degrading performance by 1.6% when gradients are blocked. On ImageNet-1K with ViT-Base, ExPLoRe improves over non-MoE baselines on two objective combinations (Token+CLS: +0.5% k-NN, +4.4% linear probe; Token+Pixel: +2.2% k-NN), achieving 80.6% linear probe and 85.3% finetuning accuracy, competitive with published methods. For downstream transfer, we develop adaptation recipes (Freeze Routing, Expert Dropout, and Freeze Attention) that improve MoE finetuning by +1.5% over the vanilla MoE, and close a 2.5--2.9 mIoU segmentation gap so that MoE models match or exceed non-MoE baselines on ADE20K.

cs.CV↗

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↗

arXiv2026

MEDiC: Multi-objective Exploration of Distillation from CLIP

Masked image modeling (MIM) methods typically operate in either raw pixel space (reconstructing masked patches) or latent feature space (aligning with a pre-trained teacher). We present MEDiC (Multi-objective Exploration of Distillation from CLIP), a framework that combines both spaces in a single pipeline through three complementary objectives: patch-level token distillation from a frozen CLIP encoder, global CLS alignment, and pixel reconstruction via a lightweight decoder. We conduct a systematic investigation of the design space surrounding this multi-objective framework. First, we show that all three objectives provide complementary information, with the full combination reaching 73.9% kNN accuracy on ImageNet-1K. Second, we introduce hierarchical clustering with relative position bias for evolved masking and find that, despite producing more semantically coherent masks than prior methods, evolved masking does not outperform simple block masking in the teacher-guided distillation setting, a finding we attribute to the teacher's inherent semantic awareness. Third, we reveal that optimal scalar loss weights are extremely fragile, with small perturbations causing drops of up to 17 percentage points in kNN accuracy. Our framework achieves 73.9% kNN and 85.1% fine-tuning accuracy with ViT-Base at 300 epochs.

cs.CV↗

arXiv2026

Spirals and Beyond: Competitive Plane Search with Multi-Speed Agents

We consider the problem of minimizing the worst-case search time for a hidden point target in the plane using multiple mobile agents of differing speeds, all starting from a common origin. The search time is normalized by the target's distance to the origin, following the standard convention in competitive analysis. The goal is to minimize the maximum such normalized time over all target locations, the search cost. As a base case, we extend the known result for a single unit-speed agent, which achieves an optimal cost of about $\mathcal{U}_1 = 17.28935$ via a logarithmic spiral, to $n$ unit-speed agents. We give a symmetric spiral-based algorithm where each agent follows a logarithmic spiral offset by equal angular phases. This yields a search cost independent of which agent finds the target. We provide a closed-form upper bound $\mathcal{U}_n$ for this setting, which we use in our general result. Our main contribution is an upper bound on the worst-case normalized search time for $n$ agents with arbitrary speeds. We give a framework that selects a subset of agents and assigns spiral-type trajectories with speed-dependent angular offsets, again making the search cost independent of which agent reaches the target. A corollary shows that $n$ multi-speed agents (fastest speed 1) can beat $k$ unit-speed agents (cost below $\mathcal{U}_k$) if the geometric mean of their speeds exceeds $\mathcal{U}_n / \mathcal{U}_k$. This means slow agents may be excluded if they lower the mean too much, motivating non-spiral algorithms. We also give new upper bounds for point search in cones and conic complements using a single unit-speed agent. These are then used to design hybrid spiral-directional strategies, which outperform the spiral-based algorithms when some agents are slow. This suggests that spiral-type trajectories may not be optimal in the general multi-speed setting.

cs.DS↗

arXiv2026

Optimal Average Disk-Inspection via Fermat's Principle

This work resolves the optimal average-case cost of the Disk-Inspection problem, a variant of Bellman's 1955 lost-in-a-forest problem. In Disk-Inspection, a mobile agent starts at the center of a unit disk and follows a trajectory that inspects perimeter points whenever the disk does not obstruct visibility. The worst-case cost was solved optimally in 1957 by Isbell, but the average-case version remained open, with heuristic upper bounds proposed by Gluss in 1961 and improved only recently. Our approach applies Fermat's Principle of Least Time to a recently proposed discretization framework, showing that optimal solutions are captured by a one-parameter family of recurrences independent of the discretization size. In the continuum limit these recurrences give rise to a single-parameter optimal control problem, whose trajectories coincide with limiting solutions of the original Disk-Inspection problem. A crucial step is proving that the optimal initial condition generates a trajectory that avoids the unit disk, thereby validating the optics formulation and reducing the many-variable optimization to a rigorous one-parameter problem. In particular, this disproves Gluss's conjecture that optimal trajectories must touch the disk. Our analysis determines the exact optimal average-case inspection cost, equal to $3.549259\ldots$ and certified to at least six digits of accuracy.

cs.DM↗

arXiv2025

Ocassionally Secure: A Comparative Analysis of Code Generation Assistants

$ $Large Language Models (LLMs) are being increasingly utilized in various applications, with code generations being a notable example. While previous research has shown that LLMs have the capability to generate both secure and insecure code, the literature does not take into account what factors help generate secure and effective code. Therefore in this paper we focus on identifying and understanding the conditions and contexts in which LLMs can be effectively and safely deployed in real-world scenarios to generate quality code. We conducted a comparative analysis of four advanced LLMs--GPT-3.5 and GPT-4 using ChatGPT and Bard and Gemini from Google--using 9 separate tasks to assess each model's code generation capabilities. We contextualized our study to represent the typical use cases of a real-life developer employing LLMs for everyday tasks as work. Additionally, we place an emphasis on security awareness which is represented through the use of two distinct versions of our developer persona. In total, we collected 61 code outputs and analyzed them across several aspects: functionality, security, performance, complexity, and reliability. These insights are crucial for understanding the models' capabilities and limitations, guiding future development and practical applications in the field of automated code generation.

cs.CR↗

arXiv2025

The Fagnano Triangle Patrolling Problem

We investigate a combinatorial optimization problem that involves patrolling the edges of an acute triangle using a unit-speed agent. The goal is to minimize the maximum (1-gap) idle time of any edge, which is defined as the time gap between consecutive visits to that edge. This problem has roots in a centuries-old optimization problem posed by Fagnano in 1775, who sought to determine the inscribed triangle of an acute triangle with the minimum perimeter. It is well-known that the orthic triangle, giving rise to a periodic and cyclic trajectory obeying the laws of geometric optics, is the optimal solution to Fagnano's problem. Such trajectories are known as Fagnano orbits, or more generally as billiard trajectories. We demonstrate that the orthic triangle is also an optimal solution to the patrolling problem. Our main contributions pertain to new connections between billiard trajectories and optimal patrolling schedules in combinatorial optimization. In particular, as an artifact of our arguments, we introduce a novel 2-gap patrolling problem that seeks to minimize the visitation time of objects every three visits. We prove that there exist infinitely many well-structured billiard-type optimal trajectories for this problem, including the orthic trajectory, which has the special property of minimizing the visitation time gap between any two consecutively visited edges. Complementary to that, we also examine the cost of dynamic, sub-optimal trajectories to the 1-gap patrolling optimization problem. These trajectories result from a greedy algorithm and can be implemented by a computationally primitive mobile agent.

cs.DM↗

arXiv2025

Disk and Partial Disk Inspection: Worst- to Average-Case and Pareto Upper Bounds

We consider $n$ unit-speed mobile agents initially positioned at the center of a unit disk, tasked with inspecting all points on the disk's perimeter. A perimeter point is considered covered if an agent located outside the disk's interior has unobstructed visibility of it, treating the disk itself as an obstacle. For $n=1$, this problem is known as the shoreline problem with a known distance. Isbell (1957) derived an optimal trajectory that minimizes the worst-case inspection time for this problem, while Gluss (1961) proposed heuristics for its average-case version. The one-agent case was originally introduced as a more tractable variant of Bellman's famous lost-in-the-forest problem. Our contributions are threefold. First, as a warm-up, we extend Isbell's findings by deriving worst-case optimal trajectories for partial inspection of a section of the disk, thereby providing an alternative proof of optimality for inspection with $n \geq 2$ agents. Second, we improve Gluss's bounds on the average-case inspection time under a uniform distribution of perimeter points (equivalent to randomized inspection algorithms), and we also strengthen the methodology by combining spatial discretization with Nonlinear Programming (NLP) to build feasible solutions to the continuous problem and compare them with NLP solutions. Third, we establish Pareto-optimal bounds for the multi-objective problem of jointly minimizing the worst-case and average-case inspection times.

cs.DM↗

arXiv2024

Makespan Trade-offs for Visiting Triangle Edges

We study a primitive vehicle routing-type problem in which a fleet of $n$unit speed robots start from a point within a non-obtuse triangle $Δ$, where $n \in \{1,2,3\}$. The goal is to design robots' trajectories so as to visit all edges of the triangle with the smallest visitation time makespan. We begin our study by introducing a framework for subdividing $Δ$into regions with respect to the type of optimal trajectory that each point $P$ admits, pertaining to the order that edges are visited and to how the cost of the minimum makespan $R_n(P)$ is determined, for $n\in \{1,2,3\}$. These subdivisions are the starting points for our main result, which is to study makespan trade-offs with respect to the size of the fleet. In particular, we define $ R_{n,m} (Δ)= \max_{P \in Δ} R_n(P)/R_m(P)$, and we prove that, over all non-obtuse triangles $Δ$: (i) $R_{1,3}(Δ)$ ranges from $\sqrt{10}$ to $4$, (ii) $R_{2,3}(Δ)$ ranges from $\sqrt{2}$ to $2$, and (iii) $R_{1,2}(Δ)$ ranges from $5/2$ to $3$. In every case, we pinpoint the starting points within every triangle $Δ$ that maximize $R_{n,m} (Δ)$, as well as we identify the triangles that determine all $\inf_ΔR_{n,m}(Δ)$ and $\sup_ΔR_{n,m}(Δ)$ over the set of non-obtuse triangles.

cs.DM↗

arXiv2024

Weighted Group Search on the Disk & Improved Lower Bounds for Priority Evacuation

We consider \emph{weighted group search on a disk}, which is a search-type problem involving 2 mobile agents with unit-speed. The two agents start collocated and their goal is to reach a (hidden) target at an unknown location and a known distance of exactly 1 (i.e., the search domain is the unit disk). The agents operate in the so-called \emph{wireless} model that allows them instantaneous knowledge of each others findings. The termination cost of agents' trajectories is the worst-case \emph{arithmetic weighted average}, which we quantify by parameter $w$, of the times it takes each agent to reach the target, hence the name of the problem. Our work follows a long line of research in search and evacuation, but quite importantly it is a variation and extension of two well-studied problems, respectively. The known variant is the one in which the search domain is the line, and for which an optimal solution is known. Our problem is also the extension of the so-called \emph{priority evacuation}, which we obtain by setting the weight parameter $w$ to $0$. For the latter problem the best upper/lower bound gap known is significant. Our contributions for weighted group search on a disk are threefold. \textit{First}, we derive upper bounds for the entire spectrum of weighted averages $w$. Our algorithms are obtained as a adaptations of known techniques, however the analysis is much more technical. \textit{Second}, our main contribution is the derivation of lower bounds for all weighted averages. This follows from a \emph{novel framework} for proving lower bounds for combinatorial search problems based on linear programming and inspired by metric embedding relaxations. \textit{Third}, we apply our framework to the priority evacuation problem, improving the previously best lower bound known from $4.38962$ to $4.56798$, thus reducing the upper/lower bound gap from $0.42892$ to $0.25056$.

cs.DM↗

arXiv2024

Multi-Agent Search-Type Problems on Polygons

We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a disk (infinite possible locations) or regular polygons (finite possible locations). Building on the foundational disk evacuation problem, the disk priority evacuation problem with $k$ Servants, and the disk $w$-weighted search problem, we make improvements on several fronts. First we establish new upper and lower bounds for the $n$-gon priority evacuation problem with $1$ Servant for $n \leq 13$, and for $n_k$-gons with $k=2, 3, 4$ Servants, where $n_2 \leq 11$, $n_3 \leq 9$, and $n_4 \leq 10$, offering tight or nearly tight bounds. The only previous results known were a tight upper bound for $k=1$ and $n=6$ and lower bounds for $k=1$ and $n \leq 9$. Second, our work improves the best lower bound known for the disk priority evacuation problem with $k=1$ Servant from $4.46798$ to $4.64666$ and for $k=2$ Servants from $3.6307$ to $3.65332$. Third, we improve the best lower bounds known for the disk $w$-weighted group search problem, significantly reducing the gap between the best upper and lower bounds for $w$ values where the gap was largest. These improvements are based on nearly tight upper and lower bounds for the $11$-gon and $12$-gon $w$-weighted evacuation problems, while previous analyses were limited only to lower bounds and only to $7$-gons.

cs.DM↗

arXiv2024

Cross-Scale MAE: A Tale of Multi-Scale Exploitation in Remote Sensing

Remote sensing images present unique challenges to image analysis due to the extensive geographic coverage, hardware limitations, and misaligned multi-scale images. This paper revisits the classical multi-scale representation learning problem but under the general framework of self-supervised learning for remote sensing image understanding. We present Cross-Scale MAE, a self-supervised model built upon the Masked Auto-Encoder (MAE).During pre-training, Cross-Scale MAE employs scale augmentation techniques and enforces cross-scale consistency constraints through both contrastive and generative losses to ensure consistent and meaningful representations well-suited for a wide range of downstream tasks. Further, our implementation leverages the xFormers library to accelerate network pre-training on a single GPU while maintaining the quality of learned representations. Experimental evaluations demonstrate that Cross-Scale MAE exhibits superior performance compared to standard MAE and other state-of-the-art remote sensing MAE methods.

cs.CV↗

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↗

arXiv2022

Triangle Evacuation of 2 Agents in the Wireless Model

The input to the \emph{Triangle Evacuation} problem is a triangle $ABC$. Given a starting point $S$ on the perimeter of the triangle, a feasible solution to the problem consists of two unit-speed trajectories of mobile agents that eventually visit every point on the perimeter of $ABC$. The cost of a feasible solution (evacuation cost) is defined as the supremum over all points $T$ of the time it takes that $T$ is visited for the first time by an agent plus the distance of $T$ to the other agent at that time. Similar evacuation type problems are well studied in the literature covering the unit circle, the $\ell_p$ unit circle for $p\geq 1$, the square, and the equilateral triangle. We extend this line of research to arbitrary non-obtuse triangles. Motivated by the lack of symmetry of our search domain, we introduce 4 different algorithmic problems arising by letting the starting edge and/or the starting point $S$ on that edge to be chosen either by the algorithm or the adversary. To that end, we provide a tight analysis for the algorithm that has been proved to be optimal for the previously studied search domains, as well as we provide lower bounds for each of the problems. Both our upper and lower bounds match and extend naturally the previously known results that were established only for equilateral triangles.

cs.DM↗

arXiv2021

Evacuating from ell_p Unit Disks in the Wireless Model

The search-type problem of evacuating 2 robots in the wireless model from the (Euclidean) unit disk was first introduced and studied by Czyzowicz et al. [DISC'2014]. Since then, the problem has seen a long list of follow-up results pertaining to variations as well as to upper and lower bound improvements. All established results in the area study this 2-dimensional search-type problem in the Euclidean metric space where the search space, i.e. the unit disk, enjoys significant (metric) symmetries. We initiate and study the problem of evacuating 2 robots in the wireless model from $\ell_p$ unit disks, $p \in [1,\infty)$, where in particular robots' moves are measured in the underlying metric space. To the best of our knowledge, this is the first study of a search-type problem with mobile agents in more general metric spaces. The problem is particularly challenging since even the circumference of the $\ell_p$ unit disks have been the subject of technical studies. In our main result, and after identifying and utilizing the very few symmetries of $\ell_p$ unit disks, we design \emph{optimal evacuation algorithms} that vary with $p$. Our main technical contributions are two-fold. First, in our upper bound results, we provide (nearly) closed formulae for the worst case cost of our algorithms. Second, and most importantly, our lower bounds' arguments reduce to a novel observation in convex geometry which analyzes trade-offs between arc and chord lengths of $\ell_p$ unit disks as the endpoints of the arcs (chords) change position around the perimeter of the disk, which we believe is interesting in its own right. Part of our argument pertaining to the latter property relies on a computer assisted numerical verification that can be done for non-extreme values of $p$.

cs.DM↗

arXiv2020

Evacuating Robots from a Disk Using Face-to-Face Communication

Assume that two robots are located at the centre of a unit disk. Their goal is to evacuate from the disk through an exit at an unknown location on the boundary of the disk. At any time the robots can move anywhere they choose on the disk, independently of each other, with maximum speed $1$. The robots can cooperate by exchanging information whenever they meet. We study algorithms for the two robots to minimize the evacuation time: the time when both robots reach the exit. In [CGGKMP14] the authors gave an algorithm defining trajectories for the two robots yielding evacuation time at most $5.740$ and also proved that any algorithm has evacuation time at least $3+ \fracπ{4} + \sqrt{2} \approx 5.199$. We improve both the upper and lower bound on the evacuation time of a unit disk. Namely, we present a new non-trivial algorithm whose evacuation time is at most $5.628$ and show that any algorithm has evacuation time at least $3+ \fracπ{6} + \sqrt{3} \approx 5.255$. To achieve the upper bound, we designed an algorithm which proposes a forced meeting between the two robots, even if the exit has not been found by either of them. We also show that such a strategy is provably optimal for a related problem of searching for an exit placed at the vertices of a regular hexagon.

cs.DS↗

arXiv2020

The Bike Sharing Problem

Assume that $m \geq 1$ autonomous mobile agents and $0 \leq b \leq m$ single-agent transportation devices (called {\em bikes}) are initially placed at the left endpoint $0$ of the unit interval $[0,1]$. The agents are identical in capability and can move at speed one. The bikes cannot move on their own, but any agent riding bike $i$ can move at speed $v_i > 1$. An agent may ride at most one bike at a time. The agents can cooperate by sharing the bikes; an agent can ride a bike for a time, then drop it to be used by another agent, and possibly switch to a different bike. We study two problems. In the \BS problem, we require all agents and bikes starting at the left endpoint of the interval to reach the end of the interval as soon as possible. In the \RBS problem, we aim to minimize the arrival time of the agents; the bikes can be used to increase the average speed of the agents, but are not required to reach the end of the interval. Our main result is the construction of a polynomial time algorithm for the \BS problem that creates an arrival-time optimal schedule for travellers and bikes to travel across the interval. For the \RBS problem, we give an algorithm that gives an optimal solution for the case when at most one of the bikes can be abandoned.

cs.DS↗