| 1. |
- Baltz, Andreas, et al.
(författare)
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Construction of Sparse Asymmetric Connectors
- 2003
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Ingår i: Proceedings of European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2003). - Berlin-Heidelberg : Springer Berlin/Heidelberg.
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Konferensbidrag (refereegranskat)
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| 2. |
- Baltz, Andreas, et al.
(författare)
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Constructions of Sparse Asymmetric Connectors with Number Theoretic Methods
- 2005
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Ingår i: Networks. - : John Wiley & Sons. - 0028-3045 .- 1097-0037. ; 45:3, s. 119-124
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of connecting a set I of n inputs to a set O of N outputs (n ≤ N) by as few edges as possible such that for every injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k . For k = Ω(log N + logn) Oruς (1994) gave the presently best (n,N)-connector with O(N+n·log n) edges. For k=2 and N the square of a prime, Richards and Hwang (1985) described a construction using edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ (N) edges, if for some ε>0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.
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| 3. |
- Baltz, Andreas, et al.
(författare)
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Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection
- 2015
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Ingår i: Journal of the Operational Research Society. - : Informa UK Limited. - 0160-5682 .- 1476-9360. ; 66:4, s. 615-626
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.
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