Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated

Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

Restricted Value Iteration: Theory and Algorithms

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this paper, we study value iteration restricted to belief subsets. We show that, together with properly chosen belief subsets, restricted value iteration yields near-optimal policies and we give a condition for determining whether a given belief subset would bring about savings in space and time. We also apply restricted value iteration to two interesting classes of POMDPs, namely informative POMDPs and near-discernible POMDPs

Jet conversions in a quark-gluon plasma

Quark and gluon jets traversing through a quark-gluon plasma not only lose their energies but also can undergo flavor conversions. The conversion rates via the elastic $q(\bar q)g\to gq(\bar q)$ and the inelastic $q\bar q\leftrightarrow gg$ scatterings are evaluated in the lowest order in QCD. Including both jet energy loss and conversions in the expanding quark-gluon plasma produced in relativistic heavy ion collisions, we have found a net conversion of quark to gluon jets. This reduces the difference between the nuclear modification factors for quark and gluon jets in central heavy ion collisions and thus enhances the $p/\pi^+$ and ${\bar p}/\pi^-$ ratios at high transverse momentum. However, a much larger net quark to gluon jet conversion rate than the one given by the lowest-order QCD is needed to account for the observed similar ratios in central Au+Au and p+p collisions at same energy. Implications of our results are discussed.Comment: version to appear in PR

Spectral constraints on unidentified EGRET gamma-ray sources from COMPTEL MeV observations

We investigated the MeV properties of 173 unidentified or only tentatively identified EGRET sources listed in the third EGRET catalogue, by analyzing the simultaneously collected COMPTEL MeV data for each individual source. The sources can generally be divided into 4 groups. In this paper we focus on one of these, a group of 22 EGRET sources for which we can provide additional constraining information: their spectral extrapolations from the energy range above 100 MeV towards lower energies overshoot the fluxes or upper limits derived simultaneously at MeV energies. This means that for these sources a spectral turnover/break between 1 MeV and 100 MeV is required. At least two of these sources, but most likely the majority of this sample, have the maxima of their gamma-ray luminosities in this energy band. The sources have rather soft EGRET spectra (average photon index: 2.72), and seem to spatially cluster in the inner Galaxy. Variability analyses revealed 11 out of the 22 sources to be significantly variable. Object classes proposed as possible counterparts for the unidentified EGRET sources are discussed in the light of these additional constraints.Comment: 9 pages including 4 figures; A&A accepte

LS 5039 - the counterpart of the unidentified MeV source GRO J1823-12

The COMPTEL experiment on CGRO observed the gamma-ray sky at energies from 0.75 MeV to 30 MeV between April 1991 and June 2000. COMPTEL detected many gamma-ray sources, among them an unidentified one labeled GRO J1823-12, which is positionally consistent with the prominent high-mass X-ray binary LS 5039. Because LS 5039 was established as gamma-ray emitter during recent years, whose gamma-radiation radiation is modulated along its binary orbit, we reanalysed the COMPTEL data of GRO J1823-12 including an orbital resolved analysis. We find a significant MeV source, showing evidence for a modulated MeV flux corresponding to the orbital period of LS 5039 of about 3.9 days. We show that its MeV emission is stronger at the orbital part around the inferior conjuction than at the part of the superior conjunction, being in phase with X-rays and TeV gamma-rays, however being in anti-phase with GeV gamma-rays. We conclude that the COMPTEL source GRO J1823-12 is the counterpart of the microquasar candidate LS 5039, at least for the majority of its MeV emission. The COMPTEL fluxes, put into multifrequency perspective, provide new constraints on the modelling of the high-energy emission of LS 5039.Comment: accepted by Astronomy & Astrophysics; 11 pages, 9 figure