- Upper Bounds on ATSP Neighborhood Size Gregory Gutin (G.Gutinrhul.ac.uk) Anders Yeo (yeodaimi.au.dk) Abstract: We consider the Asymmetric Traveling Salesman Problem (ATSP) and use the definition of neighborhood by Deineko and Woeginger (see Math. Programming 87 (2000) 519-542). Let $\mu(n)$ be the maximum cardinality of polynomial time searchable neighborhood for the ATSP on $n$ vertices. Deineko and Woeginger conjectured that $\mu (n)< \beta (n-1)!$ for any constant $\beta >0$ provided P$\neq$NP. We prove that $\mu(n) < \beta (n-k)!$ for any fixed integer $k\ge 1$ and constant $\beta >0$ provided NP$\not\subseteq$P/poly, which (like P$\neq$NP) is believed to be true. We also give upper bounds for the size of an ATSP neighborhood depending on its search time. Keywords: ATSP, TSP, exponential neighborhoods, upper bounds Category 1: Combinatorial Optimization (Graphs and Matroids ) Category 2: Combinatorial Optimization (Meta Heuristics ) Citation: Technical Report TR-01-01, Dept of Computer Science, Royal Holloway University of London, UK, April 2001 Download: [Postscript]Entry Submitted: 04/24/2001Entry Accepted: 04/24/2001Entry Last Modified: 04/24/2001Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.