Edge Elimination in TSP Instances

The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that has been solved optimally has 85,900 vertices. Its solution required more than 136 years of total CPU time using the branch-and-cut based Concorde TSP code [1]. In this paper we present graph theoretic results that allow to prove that some edges of a TSP instance cannot occur in any optimum TSP tour. Based on these results we propose a combinatorial algorithm to identify such edges. The runtime of the main part of our algorithm is $O(n^2 \log n)$ for an n-vertex TSP instance. By combining our approach with the Concorde TSP solver we are able to solve a large TSPLIB instance more than 11 times faster than Concorde alone

Diffusive behavior of a greedy traveling salesman

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d=3 and 4 the average squared distance from the origin is proportional to the number of steps t. In the d=2 case such a scaling is modified with some logarithmic corrections, which might suggest that d=2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d=2 and d>2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Levy flights. Our results suggest that broad and Levy-like distributions in such systems might appear due to dimension-dependent properties of a search space.Comment: accepted in Phys. Rev.

Mechanical Translation

Contains reports on two research projects.National Science Foundatio

Comparison of web-based and face-to-face interviews for application to an anesthesiology training program: a pilot study.

ObjectiveThis study compared admission rates to a United States anesthesiology residency program for applicants completing face-to-face versus web-based interviews during the admissions process. We also explored factors driving applicants to select each interview type.MethodsThe 211 applicants invited to interview for admission to our anesthesiology residency program during the 2014-2015 application cycle were participants in this pilot observational study. Of these, 141 applicants selected face-to-face interviews, 53 applicants selected web-based interviews, and 17 applicants declined to interview. Data regarding applicants' reasons for selecting a particular interview type were gathered using an anonymous online survey after interview completion. Residency program admission rates and survey answers were compared between applicants completing face-to-face versus web-based interviews.ResultsOne hundred twenty-seven (75.1%) applicants completed face-to-face and 42 (24.9%) completed web-based interviews. The admission rate to our residency program was not significantly different between applicants completing face-to-face versus web-based interviews. One hundred eleven applicants completed post-interview surveys. The most common reasons for selecting web-based interviews were conflict of interview dates between programs, travel concerns, or financial limitations. Applicants selected face-to-face interviews due to a desire to interact with current residents, or geographic proximity to the residency program.ConclusionsThese results suggest that completion of web-based interviews is a viable alternative to completion of face-to-face interviews, and that choice of interview type does not affect the rate of applicant admission to the residency program. Web-based interviews may be of particular interest to applicants applying to a large number of programs, or with financial limitations

A New Sub-Period-Minimum Cataclysmic Variable With Partial Hydrogen Depletion And Evidence Of Spiral Disk Structure

We present time-resolved spectroscopy and photometry of CSS 120422:111127+571239 (=SBS 1108+574), a recently discovered SU UMa-type dwarf nova whose 55 minute orbital period is well below the cataclysmic variable (CV) period minimum of similar to 78 minutes. In contrast with most other known CVs, its spectrum features He I emission of comparable strength to the Balmer lines, implying a hydrogen abundance less than 0.1 of long-period CVs-but still at least 10 times higher than that in AM CVn stars. Together, the short orbital period and remarkable helium-to-hydrogen ratio suggest that mass transfer in CSS 120422 began near the end of the donor star's main-sequence lifetime, meaning that this CV is a strong candidate progenitor of an AM CVn system as described by Podsiadlowski et al. Moreover, a Doppler tomogram of the Ha line reveals two distinct regions of enhanced emission. While one is the result of the stream-disk impact, the other is probably attributable to spiral disk structure generated when material in the outer disk achieves a 2:1 orbital resonance with respect to the donor.NSF AST-1211196, AST-9987045Department of Physics at the University of Notre DameNSF Telescope System Instrumentation Program (TSIP)Ohio Board of RegentsOhio State University Office of ResearchAstronom

Mechanical Translation

Contains research objectives and reports one two research projects.National Science Foundatio