Independent Set Under a Change Constraint from an Initial Solution
Bibliographic record
Abstract
In this paper, we study a type of incremental optimization variant of the Maximum Independent Set problem (MaxIS), called Bounded-Deletion Maximum Independent Set problem (BD-MaxIS): Given an unweighted graph $$G = (V, E)$$ , an initial feasible solution (i.e., an independent set) $$S^0\subseteq V$$ , and a non-negative integer k, the objective of BD-MaxIS is to find an independent set $$S\subseteq V$$ such that $$|S^0\setminus S|\le k$$ and |S| is maximized. The original MaxIS is generally NP-hard, but, it can be solved in polynomial time for perfect graphs (and therefore, comparability, co-comparability, bipartite, chordal, and interval graphs). In this paper, we show that BD-MaxIS is NP-hard even if the input is restricted to bipartite graphs, and hence to comparability graphs. On the other hand, fortunately, BD-MaxIS on co-comparability, interval, convex bipartite, and chordal graphs can be solved in polynomial time. Finally, we study the computational complexity on very similar variants of the Minimum Vertex Cover and the Maximum Clique problems for graph subclasses.
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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".