Directed Hamiltonicity and Out-Branchings via Generalized Laplacians
Andreas Björklund,
Petteri Kaski,
Ioannis Koutis
Abstract:We are motivated by a tantalizing open question in exact algorithms: can we detect whether an n-vertex directed graph G has a Hamiltonian cycle in time significantly less than 2 n ?We present new randomized algorithms that improve upon several previous works: a. We show that for any constant 0 < λ < 1 and prime p we can count the Hamiltonian cycles modulo p ⌊(1−λ) n 3p ⌋ in expected time less than c n for a constant c < 2 that depends only on p and λ. Such an algorithm was previously known only for the case of… Show more
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