Bibliographic record
Abstract
This paper compares several published algorithms which list all of the maximal cliques of a graph. A clique is a complete subgraph, i.e., a set of vertices and edges such that every pair of vertices is joined by an edge. A maximal clique is a clique which is not a proper subgraph of a larger clique. A closely related concept is that of a maximal independent set (MIS), where every pair of vertices is lacking an edge. An algorithm which lists maximal cliques for a graph G can also list MISs of graph G, if the input is changed from G to the complement of G, i.e., each edge is converted to a nonedge and vice versa. Many algorithms have been developed for finding all of the maximal cliques or MISs of a graph, but few papers compare more than a couple of these algorithms experimentally. Some papers give theoretical bounds on the complexity of algorithms, but improved theoretical bounds do not always translate into improved practical performance. This state of affairs makes it difficult for a researcher looking for the fastest algorithm to list all the maximal cliques of a graph. In this paper we compare five clique- or MIS-listing algorithms, and show that variations of the Bron and Kerbosch algorithm appear to be the fastest for random graphs and a type of graph which arises in physical mapping of genomes. Introduction: Clique- and MIS-listing algorithms
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.001 |
| 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 | 0.001 |
| Open science | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".