Complexity dichotomy on partial grid recognition

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even trivial. A natural step, outstanding thus far, was to provide a broad classification of graphs that make for polynomial or NP-complete instances. We provide such a classification based on the set of allowed vertex degrees in the input graphs, yielding a full dichotomy on the complexity of the problem. As byproducts, the previous NP-completeness result for binary trees was strengthened to strictly binary trees, and the three-dimensional version of the problem was for the first time proven to be NP-complete. Our results were made possible by introducing the concepts of consistent orientations and robust gadgets, and by showing how the former allows NP-completeness proofs by local replacement even in the absence of the latter

Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete

We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O(\sqrt{n}) distance and an optimal energy spanner. This is one of the most interesting restrictions of Metric Dimension in the context of wireless multi-hop networks.Comment: A brief announcement of this result has been published in the proceedings of ALGOSENSORS 201

Galaxy cluster mergers as triggers for the formation of jellyfish galaxies: case study of the A901/2 system

The A901/2 system is a rare case of galaxy cluster interaction, in which two galaxy clusters and two smaller groups are seen in route of collision with each other simultaneously. Within each of the four substructures, several galaxies with features indicative of jellyfish morphologies have been observed. In this paper, we propose a hydrodynamic model for the merger as a whole, compatible with its diffuse X-ray emission, and correlate the gas properties in this model with the locations of the jellyfish galaxy candidates in the real system. We find that jellyfish galaxies seem to be preferentially located near a boundary inside each subcluster where diffuse gas moving along with the subcluster and diffuse gas from the remainder of the system meet. The velocity change in those boundaries is such that a factor of up to $\sim$1000 increase in the ram pressure takes place within a few hundred kpc, which could trigger the high rate of gas loss necessary for a jellyfish morphology to emerge. A theoretical treatment of ram pressure stripping in the environment of galaxy cluster mergers has not been presented in the literature so far; we propose that this could be a common scenario for the formation of jellyfish morphologies in such systems.Comment: Accepted for publication in MNRAS. 10 pages, 9 figure

Advanced Vehicle Tracking system using GSM/GPRS and GPS

Vehicle Tracker is a Universal Anti-Larceny System for all kinds of motorcycles. The gadget is inserted inside a vehicle whose position is to be resolved and followed continuously. The composed device works utilizing Global Positioning System (GPS) and Global system for mobile communication/General Packet Radio Service (GSM/GPRS) technology that is the most widely recognized courses for vehicle tracking system. GPS and high sensitivity antenna are used for effective and precise location tracking of motorcycle through mobile application. Accelerometer sensor will alert the user of a possible larceny by detecting the slightest transition of the motorcycle. Immobilizer relay to remotely enable/incapacitate motorcycle ignition. Ignition switch status monitoring is utilized to detect key insertion. Fuel level sensor used to detect fuel larceny and to determine the information about fuel level in automobile tank

Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model

We consider the self-assembly of fractals in one of the most well-studied models of tile based self-assembling systems known as the Two-handed Tile Assembly Model (2HAM). In particular, we focus our attention on a class of fractals called discrete self-similar fractals (a class of fractals that includes the discrete Sierpi\'nski carpet). We present a 2HAM system that finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1. Moreover, the 2HAM system that we give lends itself to being generalized and we describe how this system can be modified to obtain a 2HAM system that finitely self-assembles one of any fractal from an infinite set of fractals which we call 4-sided fractals. The 2HAM systems we give in this paper are the first examples of systems that finitely self-assemble discrete self-similar fractals at scale factor 1 in a purely growth model of self-assembly. Finally, we show that there exists a 3-sided fractal (which is not a tree fractal) that cannot be finitely self-assembled by any 2HAM system

Optimal self-assembly of finite shapes at temperature 1 in 3D

Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for an arbitrary finite, connected shape $X \subset \mathbb{Z}^2$, there is a tile set that uniquely self-assembles into a 3D representation of a scaled-up version of $X$ at temperature 1 in 3D with optimal program-size complexity (the "program-size complexity", also known as "tile complexity", of a shape is the minimum number of tile types required to uniquely self-assemble it). Moreover, our construction is "just barely" 3D in the sense that it only places tiles in the $z = 0$ and $z = 1$ planes. Our result is essentially a just-barely 3D temperature 1 simulation of a similar 2D temperature 2 result by Soloveichik and Winfree (SICOMP 2007)