On approximating a new generalization of traveling salesman problem.

The current best-known performance guarantees for the extensively studied Traveling Salesman Problem (TSP) of determinate approximation algorithms is 32, achieved by Christofides' algorithm 47 years ago. This paper investigates a new generalization problem of the TSP, termed the Minimum-Cost Bounded Degree Connected Subgraph (MBDCS) problem. In the MBDCS problem, the goal is to identify a minimum-cost connected subgraph containing n=|V| edges from an input graph G=(V,E) with degree upper bounds for particular vertices. We show that for certain special cases of MBDCS, the aim is equivalent to finding a minimum-cost Hamiltonian cycle for the input graph, same as the TSP. To appropriately solve MBDCS, we initially present an integer programming formulation for the problem. Subsequently, we propose an algorithm to approximate the optimal solution by applying the iterative rounding technique to solution of the integer programming relaxation. We demonstrate that the returned subgraph of our proposed algorithm is one of the best guarantees for the MBDCS problem in polynomial time, assuming P≠NP. This study views the optimization of TSP as finding a minimum-cost connected subgraph containing n edges with degree upper bounds for certain vertices, and it may provide new insights into optimizing the TSP in future research.

[Investigation on the Possibility of EGFR Mutation Testing on DNA Extracted from Fixation Liquid of Lung Cancer Biopsy].

BACKGROUND: Epidermal growth factor receptor (EGFR) mutation is the most common gene mutation in patients with non-small cell lung cancer (NSCLC). Many international guidelines are recommended to detected the EGFR mutation before the treatment of advanced non-small cell lung cancer. To investigate the possibility of EGFR mutation testing on DNA extracted from fixation liquid of lung cancer biopsy. METHODS: Fixation liquid of lung cancer biopsy was collected and stored at -80 oC after centrifugal. DNA was extracted and EGFR gene mutation was detected by ARMS. Compared with EGFR mutation status of paraffin-embedded tissues, the consistency, the sensitivity and specificity of EGFR mutation testing were analyzed. RESULTS: Among the 28 cases of EGFR mutation positive and 20 cases of EGFR mutation negative previously tested on paraffin-embedded tissue by clinic test, 20 cases with EGFR mutation positive and 20 cases with negative were detected by matched fixation liquid of lung cancer biopsy, respectively. The sensitivity and specificity were 71.4% and 100%. Moreover, 52 paraffin-embedded tissues and matched fixation liquid of lung cancer biopsy with unknown EGFR mutation status were detected, and the EGFR mutation positive rate were 36.5% and 28.8% respectively. The sensitivity and specificity of fixation liquid of lung cancer biopsy were 78.9% and 100.0%. CONCLUSIONS: Extracting the DNA from fixation liquid of lung cancer biopsy may be a kind of feasible way to detect EGFR mutation.