Dissertation/ Thesis
Algorithms and complexity for approximately counting hypergraph colourings and related problems
| Τίτλος: | Algorithms and complexity for approximately counting hypergraph colourings and related problems |
|---|---|
| Συγγραφείς: | Wang, Jiaheng |
| Συνεισφορές: | Guo, Heng, Cryan, Mary |
| Στοιχεία εκδότη: | University of Edinburgh, 2024. |
| Έτος έκδοσης: | 2024 |
| Θεματικοί όροι: | Algorithms, complexity, counting hypergraph colourings, approximately counting hypergraph colourings, constraint satisfaction problems (CSPs), local lemma regime, hypergraph colouring |
| Περιγραφή: | The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of Lovász local lemma when Δ ≲ qᵏ. In prior, however, fast approximate counting algorithms exist when Δ ≲ qᵏ/³, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. • When q, k ≥ 4 are evens and Δ ≥ 5·qᵏ/², approximating the number of hypergraph colourings is NP-hard. • When the input hypergraph is linear and Δ ≲ qᵏ/², a fast approximate counting algorithm does exist. |
| Τύπος εγγράφου: | Thesis Or Dissertation |
| Γλώσσα: | English |
| DOI: | 10.7488/era/4124 |
| Σύνδεσμος πρόσβασης: | https://ethos.blethoshyku.com/concern/thesis_or_dissertations/893523 |
| Αριθμός Καταχώρησης: | edsble.893523 |
| Βάση Δεδομένων: | British Library EThOS |
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