Algorithmic complexity and extremality characterizations for edge searching and its variations
Bibliographic record
Abstract
Edge searching is a combinatorial game played on graphs. The aim is to construct a search strategy to catch an intruder hidden in the graph independent of his actions. If the intruder has a diffused form then searching corresponds to cleaning the graph. A related problem consists of minimizing the number of searchers used in this search. Various versions of edge searching have been introduced in the past depending on how searchers and the intruder can move. In this dissertation we define Weighted Search and Fast Search as two new variants and answer some complexity and extremality problems. -- Weighted Search corresponds to cleaning a contaminated graph where edges may have different capacities. The main result we have is that Weighted Search is an NP-complete problem. We also give comparison results such as bounds on the weighted search number in terms of related graph parameters including pathwidth. We characterize those graphs which two searchers can clean. -- Fast Search is an internal monotone search where no edge is traversed more than once in a non-weighted graph. We present a linear time algorithm to compute a fast search strategy for a given tree. We investigate the fast search strategies for bipartite graphs. -- The construction of k-searchable graphs, those graphs which k searchers can clean, has been of major interest. Graphs that are 1,2 or 3-searchable have been completely characterized previously, whereas characterizing 4-searchable graphs was left as an open problem. We solve this problem partially and give insights for future work.
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 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 | 0.003 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.012 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.007 | 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".