Faster exponential-time algorithms in graphs of bounded average degree

We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation suppresses factors polynomial in the input size. Thus, we generalize the recent results of Bjorklund et al. [TALG 2012] on graphs of bounded degree. Then, we move to the problem of counting perfect matchings in a graph. We first present a simple algorithm for counting perfect matchings in an n-vertex graph in O*(2^{n/2}) time and polynomial space; our algorithm matches the complexity bounds of the algorithm of Bjorklund [SODA 2012], but relies on inclusion-exclusion principle instead of algebraic transformations. Building upon this result, we show that the number of perfect matchings in an n-vertex graph with average degree bounded by d can be computed in O*(2^{(1-\eps_{2d})n/2}) time and exponential space, where \eps_{2d} is the constant obtained by us for the Traveling Salesman Problem in graphs of average degree at most 2d. Moreover we obtain a simple algorithm that counts the number of perfect matchings in an n-vertex bipartite graph of average degree at most d in O*(2^{(1-1/(3.55d))n/2}) time, improving and simplifying the recent result of Izumi and Wadayama [FOCS 2012].Comment: 10 page

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

Synthetic aperture radar target simulator

A simulator for simulating the radar return, or echo, from a target seen by a SAR antenna mounted on a platform moving with respect to the target is described. It includes a first-in first-out memory which has digital information clocked in at a rate related to the frequency of a transmitted radar signal and digital information clocked out with a fixed delay defining range between the SAR and the simulated target, and at a rate related to the frequency of the return signal. An RF input signal having a frequency similar to that utilized by a synthetic aperture array radar is mixed with a local oscillator signal to provide a first baseband signal having a frequency considerably lower than that of the RF input signal

The elusive old population of the dwarf spheroidal galaxy Leo I

We report the discovery of a significant old population in the dwarf spheroidal (dSph) galaxy Leo I as a result of a wide-area search with the ESO New Technology Telescope. Studies of the stellar content of Local Group dwarf galaxies have shown the presence of an old stellar population in almost all of the dwarf spheroidals. The only exception was Leo I, which alone appeared to have delayed its initial star formation episode until just a few Gyr ago. The color-magnitude diagram of Leo I now reveals an extended horizontal branch, unambiguously indicating the presence of an old, metal-poor population in the outer regions of this galaxy. Yet we find little evidence for a stellar population gradient, at least outside R > 2' (0.16 kpc), since the old horizontal branch stars of Leo I are radially distributed as their more numerous intermediate-age helium-burning counterparts. The discovery of a definitely old population in the predominantly young dwarf spheroidal galaxy Leo I points to a sharply defined first epoch of star formation common to all of the Local Group dSph's as well as to the halo of the Milky Way.Comment: 4 pages, 3 postscript figures, uses apjfonts.sty, emulateapj.sty. Accepted for publication in ApJ Letter

External calibration of SIR-B imagery with area-extended and point targets

Data-takes on two ascending orbits of the Shuttle Imaging Radar-B (SIR-B) over an agricultural test site in west-central Illinois were used to establish end-to-end transfer functions for conversion of the digital numbers on the 8-bit image to values of the radar backscattering coefficient sigma sup 0 (sq m/sq. m) in dB. The transfer function for each data-take was defined by the SIR-B response to an array of six calibrated point targets of known radar cross-section (transponders) and to a large number of area-extended targets also with known radar cross-section as measured by externally calibrated, truck-mounted scatterometers. The radar cross-section of each transponder at the SIR-B center frequency was measured on an antenna range as a function of local angle of incidence. Two truck-mounted scatterometers observed 20 to 80 agricultural fields daily at 1.6 GHz with HH polarization and at azimuth viewing angles and incidence angles equivalent to those of the SIR-B. The form of the transfer function is completely defined by the SIR-B receiver and the incoherent averaging procedure incorporated into production of the standard SIR-B image product

On the HI-Hole and AGB Stellar Population of the Sagittarius Dwarf Irregular Galaxy

Using two HST/ACS data-sets that are separated by ~2 years has allowed us to derive the relative proper-motion for the Sagittarius dwarf irregular (SagDIG) and reduce the heavy foreground Galactic contamination. The proper-motion decontaminated SagDIG catalog provides a much clearer view of the young red-supergiant and intermediate-age asymptotic giant branch populations. We report the identification of 3 Milky Way carbon-rich dwarf stars, probably belonging to the thin disk, and pointing to the high incidence of this class at low Galactic latitudes. A sub-group of 4 oxygen-rich candidate stars depicts a faint, red extension of the well-defined SagDIG carbon-rich sequence. The origin of these oxygen-rich candidate stars remains unclear, reflecting the uncertainty in the ratio of carbon/oxygen rich stars. SagDIG is also a gas-rich galaxy characterized by a single large cavity in the gas disk (HI-hole), which is offset by ~360 pc from the optical centre of the galaxy. We nonetheless investigate the stellar feedback hypothesis by comparing the proper-motion cleaned stellar populations within the HI-hole with appropriately selected comparison regions, having higher HI densities external to the hole. The comparison shows no significant differences. In particular, the centre of the HI-hole (and the comparison regions) lack stellar populations younger than ~400 Myr, which are otherwise abundant in the inner body of the galaxy. We conclude that there is no convincing evidence that the SagDIG HI-hole is the result of stellar feedback, and that gravitational and thermal instabilities in the gas are the most likely mechanism for its formation.Comment: Accepted for publication in A&A, 11 pages, 6 jpeg figure

On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

Complete Experimental Structure Determination of the p(3x2)pg Phase of Glycine on Cu{110}

We present a quantitative low energy electron diffraction (LEED) surface-crystallograpic study of the complete adsorption geometry of glycine adsorbed on Cu{110} in the ordered p(3×2) phase. The glycine molecules form bonds to the surface through the N atoms of the amino group and the two O atoms of the de-protonated carboxylate group, each with separate Cu atoms such that every Cu atom in the first layer is involved in a bond. Laterally, N atoms are nearest to the atop site (displacement 0.41 Å). The O atoms are asymmetrically displaced from the atop site by 0.54 Å and 1.18 Å with two very different O-Cu bond lengths of 1.93 Å and 2.18 Å. The atom positions of the upper-most Cu layers show small relaxations within 0.07 Å of the bulk-truncated surface geometry. The unit cell of the adsorbate layer consists of two glycine molecules, which are related by a glide-line symmetry operation. This study clearly shows that a significant coverage of adsorbate structures without this glide-line symmetry must be rejected, both on the grounds of the energy dependence of the spot intensities (LEED-IV curves) and of systematic absences in the LEED pattern