Broadcasting in Stars of Cliques and Path-Connected Cliques
Why this work is in the frame
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Bibliographic record
Abstract
Broadcasting is a fundamental information dissemination problem in a connected network where one node, referred to as the originator, must distribute a message to all other nodes through a series of calls along the network’s links. Once informed, nodes assist the originator by forwarding the message to their neighbors. Determining the broadcast time for a node in an arbitrary network is NP-complete. While polynomial-time algorithms exist for specific network topologies, the problem remains open for many others. In this paper, we focus on addressing the broadcasting problem in network topologies represented by specialized clique-based structures. Specifically, we investigate the windmill graph Wdk,l, which consists of k cliques of size l connected to a universal node, and extend our study to the star of cliques, a generalization of the windmill graph with cliques of arbitrary sizes. Our primary objective is to propose an efficient algorithm for determining the broadcast time of any node in an arbitrary star of cliques and to rigorously prove its optimality. Additionally, we broaden the scope by examining the broadcasting problem in path-connected cliques, a topology featuring k cliques of varying sizes sequentially connected along a path. For this structure, we develop a computationally efficient algorithm that leverages clique sizes and adjacency to optimize broadcast strategies, with broader implications for understanding communication in block graphs.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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