6533b82dfe1ef96bd12915bc
RESEARCH PRODUCT
Minimal Absent Words in Rooted and Unrooted Trees
Paweł GawrychowskiGabriele Ficisubject
Polynomial (hyperelastic model)050101 languages & linguistics05 social sciencesComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)02 engineering and technologyCombinatoricsTree (descriptive set theory)CardinalityInteger0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0501 psychology and cognitive sciencesAlphabetMinimal Absent Words Rooted trees Unrooted Trees AlgorithmsNonlinear Sciences::Pattern Formation and SolitonsComputer Science::Formal Languages and Automata TheoryMathematicsdescription
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet \(\varSigma \) of cardinality \(\sigma \). We show that the set \(\text {MAW}(T)\) of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality \(O(n\sigma )\) (resp. \(O(n^{2}\sigma )\)), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time \(O(n+|\text {MAW}(T)|)\) (resp. \(O(n^{2}+|\text {MAW}(T)|)\) assuming an integer alphabet of size polynomial in n.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 |