Communication costs in a geometric communication network
Bibliographic record
Abstract
We represent a communication network as a graph in which each node has only local information about the graph, except for an upper bound on the number of nodes, and nodes communicate by passing messages along its edges. Here, we consider a geometric communication network where the nodes also occupy points in space and the distance between points is the Euclidean distance. Our goal is to understand the communication cost needed to solve several fundamental geometry problems, including Farthest Pair, Convex Hull, Closest Pair, and approximations of these problems, in the asynchronous CONGEST KT1 model, where each node knows its ID and those of its neighbors. This extends the 2011 result of Rajsbaum and Urrutia for finding a convex hull of a planar geometric communication network to networks of arbitrary topology. We define a new model where each node has a position on the plane and nodes can communicate to each other if and only if there is an edge between them. We motivate the model and study a number of geometric problems in this model. We prove lower bounds on the communication complexity of the problems in this new model and present approximation algorithms for them. We prove lower bounds on the number of expected bits required for any randomized algorithm to solve the problems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".