Sequencing of insertions in printed circuit board assembly
Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing in Science and Engineering
Approximation algorithms for NMR spectral peak assignment
Theoretical Computer Science
Automated Protein NMR Resonance Assignments
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Simple Algorithms for Gilmore–Gomory's Traveling Salesman and Related Problems
Journal of Scheduling
A random graph approach to NMR sequential assignment
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
On Gilmore-Gomory's open question for the bottleneck TSP
Operations Research Letters
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Consider a truck running along a road. It picks up a load Li at point βi and delivers it at αi, carrying at most one load at a time. The speed on the various parts of the road in one direction is given by f(x) and that in the other direction is given by g(x). Minimizing the total time spent to deliver loads L1,...,Ln is equivalent to solving the Traveling Salesman Problem (TSP) where the cities correspond to the loads Li with coordinates (αi, βi) and the distance from Li to Lj is given by $\int^{\beta_j}_{\alpha_i} f(x)dx$ if βj ≥ αi and by $\int^{\alpha_i}_{\beta_j} g(x)dx$ if βj αi. This case of TSP is polynomially solvable with significant real-world applications. Gilmore and Gomory obtained a polynomial time solution for this TSP [6]. However, the bottleneck version of the problem (BTSP) was left open. Recently, Vairaktarakis showed that BTSP with this distance metric is NP-complete [10]. We provide an approximation algorithm for this BTSP by exploiting the underlying geometry in a novel fashion. This also allows for an alternate analysis of Gilmore and Gomory's polynomial time algorithm for the TSP. We achieve an approximation ratio of (2+γ) where $\gamma \geq \frac{f(x)}{g(x)} \geq \frac{1}{\gamma} \; \forall x$. Note that when f(x)=g(x), the approximation ratio is 3.