Bounding Interference in Wireless Ad Hoc Networks With Nodes in Random Position
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Bibliographic record
Abstract
Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected while minimizing the maximum (respectively, average) interference. We consider the model introduced by von Rickenbach (2005), in which each wireless node is represented by a point in Euclidean space on which is centered a transmission range represented by a ball, and edges in the corresponding graph are symmetric. The problem is NP-complete in two or more dimensions (Buchin 2008), and no polynomial-time approximation algorithm is known. We show how to solve the problem efficiently in settings typical for wireless ad hoc networks. If nodes are represented by a set P of n points selected uniformly and independently at random over a d-dimensional rectangular region, then the topology given by the closure of the Euclidean minimum spanning tree of P has O(log n) maximum interference with high probability and O(1) expected interference. We extend the first bound to a general class of communication graphs over a broad set of probability distributions. We present a local algorithm that constructs a graph from this class; this is the first local algorithm to provide an upper bound on expected maximum interference. Finally, we disprove a conjecture of Devroye and Morin (2012) relating the maximum interference of the Euclidean minimum spanning tree to the optimal maximum interference attainable.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it