Improving Christofides' Algorithm for the s-t Path TSP

We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5/3-approximation algorithm for this problem, and this asymptotically tight bound in fact has been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held-Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of the path-variant Held-Karp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prize-collecting s-t path problem and the unit-weight graphical metric s-t path TSP.Comment: 31 pages, 5 figure

Spectral centrality measures in complex networks

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank, eigenvector centrality and the hub/authority scores of HITS. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.Comment: 11 pages, 10 figures, 5 tables. Final version published in Physical Review

The development of the Canadian Mobile Servicing System Kinematic Simulation Facility

Canada will develop a Mobile Servicing System (MSS) as its contribution to the U.S./International Space Station Freedom. Components of the MSS will include a remote manipulator (SSRMS), a Special Purpose Dexterous Manipulator (SPDM), and a mobile base (MRS). In order to support requirements analysis and the evaluation of operational concepts related to the use of the MSS, a graphics based kinematic simulation/human-computer interface facility has been created. The facility consists of the following elements: (1) A two-dimensional graphics editor allowing the rapid development of virtual control stations; (2) Kinematic simulations of the space station remote manipulators (SSRMS and SPDM), and mobile base; and (3) A three-dimensional graphics model of the space station, MSS, orbiter, and payloads. These software elements combined with state of the art computer graphics hardware provide the capability to prototype MSS workstations, evaluate MSS operational capabilities, and investigate the human-computer interface in an interactive simulation environment. The graphics technology involved in the development and use of this facility is described

Memory detection 2.0: the first web-based memory detection test

There is accumulating evidence that reaction times (RTs) can be used to detect recognition of critical (e.g., crime) information. A limitation of this research base is its reliance upon small samples (average n = 24), and indications of publication bias. To advance RT-based memory detection, we report upon the development of the first web-based memory detection test. Participants in this research (Study1: n = 255; Study2: n = 262) tried to hide 2 high salient (birthday, country of origin) and 2 low salient (favourite colour, favourite animal) autobiographical details. RTs allowed to detect concealed autobiographical information, and this, as predicted, more successfully so than error rates, and for high salient than for low salient items. While much remains to be learned, memory detection 2.0 seems to offer an interesting new platform to efficiently and validly conduct RT-based memory detection research

Improved Bounds on Information Dissemination by Manhattan Random Waypoint Model

With the popularity of portable wireless devices it is important to model and predict how information or contagions spread by natural human mobility -- for understanding the spreading of deadly infectious diseases and for improving delay tolerant communication schemes. Formally, we model this problem by considering $M$ moving agents, where each agent initially carries a \emph{distinct} bit of information. When two agents are at the same location or in close proximity to one another, they share all their information with each other. We would like to know the time it takes until all bits of information reach all agents, called the \textit{flood time}, and how it depends on the way agents move, the size and shape of the network and the number of agents moving in the network. We provide rigorous analysis for the \MRWP model (which takes paths with minimum number of turns), a convenient model used previously to analyze mobile agents, and find that with high probability the flood time is bounded by $O\big(N\log M\lceil(N/M) \log(NM)\rceil\big)$, where $M$ agents move on an $N\times N$ grid. In addition to extensive simulations, we use a data set of taxi trajectories to show that our method can successfully predict flood times in both experimental settings and the real world.Comment: 10 pages, ACM SIGSPATIAL 2018, Seattle, U