Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2109.12185

Message Delivery in the Plane by Robots with Different Speeds

Jared Coleman·Evangelos Kranakis·Danny Krizanc·Oscar Morales-Ponce
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 $1.0405$.

Explore related subjects

cs.DCcs.DM

Keep this discovery

BibTeXRIS

Jared Coleman, Evangelos Kranakis, Danny Krizanc, Oscar Morales-Ponce. 2021-09-24. Message Delivery in the Plane by Robots with Different Speeds. https://arxiv.org/abs/2109.12185

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Online Treasure Hunt in Vertex-Permuted Dynamic Rings

We study the problem of treasure hunt by a group of $k \geq 1$ agents in vertex-permuted dynamic rings (VP). In this model, the $n$ vertices remain on a ring but are permuted at each time step. We first show that treasure hunt is impossible for any $k \leq n-3$ agents, if there are no restrictions on the sequence of permutations used in the dynamic ring. We then study the $VP(\delta)$ setting, in which for every pair $i, j$ of vertices, the edge $(i, j)$ is guaranteed to appear within $\delta$ steps. We show that the class $VP(\delta)$ is feasible only for $\delta \geq \left\lceil \frac{n-1}{2}\right\rceil$. For the one-agent case, we show a tight bound of $\Theta(\delta n)$ on the worst-case search time as well as competitive ratio of any online algorithm for treasure hunt, provided $\delta \geq 2n$. We then give an optimal algorithm for $k$ agents, thereby showing that $k$ agents can obtain a speedup of $k$ on the worst-case search time. Finally, in the R-VP setting, in which in every step, the vertices are arranged as a ring according to a random permutation, we show that treasure hunt takes expected $\Theta(n)$ steps against an oblivious adversary and $\Theta(n \log n)$ steps against an adaptive adversary.

cs.DC↗
arXiv2026

The Computing Channel: How Modulation Programs the Airwaves

Distributed computing and distributed artificial intelligence require frequent exchanges of intermediate results, although many applications need only an aggregate rather than messages from individual devices. Conventional systems recover each message before computing the aggregate, whereas over-the-air computation (OAC) exploits simultaneous transmission to obtain it directly. However, dominant OAC implementations rely on analog signaling, creating a mismatch with finite-precision data and digital communication procedures. This article presents digital function-oriented communication, in which finite-alphabet symbol representations and receiver decisions are jointly designed so that multiple-access superposition encodes the desired function without recovering individual inputs. We introduce its computational-constellation principle, main design approaches, extensions, and implementation challenges. Federated edge learning illustrates how the framework can reduce user-dependent data-bearing resources while operating directly on quantized model updates.

cs.DC↗
arXiv2026

Can AI Remediate Backend Failures Safely? GuardedAct with Blast-Radius-Aware Sandboxing

Large Language Models (LLMs) have shown promising capabilities in generating remediation actions for microservice failures. However, directly executing AI-generated repair actions in production risks cascading collateral damage. We propose GuardedAct, a sandbox-first remediation framework that interposes a blast-radius-aware verification layer between the LLM action generator and the production environment. GuardedAct operates in four phases: (1) ingesting a diagnosis report together with the live system topology and recent telemetry, (2) prompting an LLM to produce a ranked list of candidate remediation actions, (3) simulating each action in a lightweight digital-twin sandbox that estimates the blast radius and assigns a risk label, and (4) enforcing a rollback-confidence gate that auto-executes only low-risk actions while escalating high-risk ones for human review. We evaluate GuardedAct on five fault scenarios injected into the DeathStarBench social-network application. Experimental results show that GuardedAct achieves an overall recovery rate of 87.4% while reducing collateral damage by 79.7% relative to direct LLM execution (from 25.6% to 5.2%), at the cost of a modest sandbox-induced increase in mean time to recovery (approximately 8 s). Ablation studies confirm that each component contributes meaningfully to the safety-speed trade-off.

cs.DC↗