Updated index.rst

index.rst

@@ -407,6 +407,8 @@ On the other hand, pedestrian networks are as important as transportation networ
 		58.4 Complexity Measures for Map-Reduce and Comparison to Parallel Computing - https://users.cs.duke.edu/~kamesh/mapreduce.pdf
 		58.5 Efficient Circuit Simulation in MapReduce - [Fabian Frei-Koichi Wada] - https://arxiv.org/pdf/1907.01624.pdf - "... Relying on the standard MapReduce model introduced by Karloff et al. a decade ago, we develop an intricate simulation technique to show that any problem in NC (i.e., a problem solved by a logspace-uniform family of Boolean circuits of polynomial size and a depth polylogarithmic in the input size) can be solved by a MapReduce computation in O(T(n)/ log n) rounds, where n is the input size and T(n) is the depth of the witnessing circuit family. Thus, we are able to closely relate the standard, uniform NC hierarchy modeling parallel computations to the deterministic MapReduce hierarchy DMRC by proving that NCi+1 ⊆ DMRCi for all i ∈ N ..." - NC circuit of depth O((logN)^(i+1)) is in DMRCi which is an improvement over 58.1. Computational Geometric Factorization Spark MapReduce implementation in NeuronRain is of polylogdepth or runtime O((logN)^(k+1)) and thus in NC^2=DMRC1 for k=1. Due to this result, underlying parallel hardware model (Multicore-PRAM-BSP-logP) is abstracted and MapReduce frameworks are sufficient to implement NC.
 		58.6 Sorting, Searching, and Simulation in the MapReduce Framework - [Goodrich-Sitchinava-Zhang] - https://arxiv.org/pdf/1101.1902.pdf - "... Lemma 4.3: Given a set X of N indexed comparable items, we can sort them in O(logM(N)) rounds and O(N^2*logM(N)) communication complexity in the MapReduce model. ..." - Computational Geometric Factorization implemented in NeuronRain is a Parallel Planar Point Location Binary Search algorithm which does not require sorting as every rectified hyperbolic arc segment is locally binary (or interpolation) searched. Even if sorting is necessary, by this result, factors could be found in O(logM(N)+logN) time having an additional sequential binary search overhead after sorting. 
+                58.7 Comparison between DOT, BSP, PRAM, MapReduce, Dryad, MUD, MRC, NC models - slide 31 - Complexity class separations - https://prezi.com/qeiah0kue1il/comparison-between-dot-and-other-big-data-analytic-models/ - DMRC is strictly contained in P while NC and DMRC problems overlap to large extent which implies even if MapReduce DMRC implementation of Computational Geometric Parallel Planar Point Location Factorization algorithm may not be exactly in NC (though algorithm adheres to definition of NC by parallel binary search of O((logN)^k) tile segments each in O(N/(logN)^k) processors), it is strictly in P (best possible under hardware limitations) and all benchmark numbers for Primality and Factorization are of polynomial time (in number of bits or input size - O((logN)^k)).
+                58.8 NC Parallel complexity class and Supercomputing - https://web.ece.ucsb.edu/~parhami/pres_folder/f32-book-parallel-pres-pt1.pdf - Datacenter as a Computer - http://web.eecs.umich.edu/~mosharaf/Readings/DC-Computer.pdf - Section 2.5.3 - Google Scholar article similarity 
 	59. Almost all Autonomous Drone Delivery Problems including Drone Electronic Voting Machines, Online Shopping Delivery, Autonomous Combat Drone Swarms are NP-Complete which have to navigate along Hamiltonians optimally on surface and aerial transportation graphs. NeuronRain theory describes a Graph Masking Drone Obstacle Avoidance algorithm by dynamically overlaying segmented (convexhull) weather GIS imagery on terrestrial transportation graph for weather obstacles which is crucial for faultless delivery of payload carried by drones. Graph Masking which is a computational geometric planar intersection problem of graph and convex hull polygons, removes (or masks) subgraphs below aerial weather obstacles (e.g cloud) from transportation graph thereby creating a stripped-down topologically punctured transportation graph which bypasses weather obstacles. Optimal best route in this masked transportation graph could be found by A* Best First Search Robotic Motion Planning algorithm. Segmenting wind speed and temperature obstacle convex hulls from Weather GIS imagery is non-trivial because of high fluidity of atmosphere. Obstacles for UAVs are two fold - Natural (Inclement weather, Mountains) and Artificial (Man-made structures). Artificial obstacles can be avoided by choosing airstrip directly above surface transportation graph edges (Road network) as airspace above roads is usually free of obstacles and structures except interchanges which could be bypassed by raising drone altitude to atleast the maximum height of the structures. Natural obstacles (Rains, Wind, Heat) are not so obvious to tackle - Though cloud formations in Weather GIS are somewhat static and can be bounded by convex hull polygon boxes, segmenting wind and heat obstacle convex hulls requires sensors transmitting wind speed and temperature either from Satellite GIS or from points on Road network. Gathering wind and heat data along the points on transportation graph minimizes number of sensors. Onboard sensors in Drones for wind and heat may not be sufficient because drone has to learn obstacle data which are located at some distance ahead from drones so as to backtrack and realign the mission trajectory. Obstacle Avoidance Algorithms in Drone Navigation apply as well with some modifications to Advanced Driver Assistance Systems (ADAS) for self-driving surface transport automobiles (e.g lane detection, collision detection). An example primitive self-driving collision detection algorithm for LIDAR sensor and GPS based ADAS (requires a realtime OS kernel for low response time - a primitive C++ and Python usecase for LIDAR PCD generated obstacle-free lattice walks has been implemented in NeuronRain AstroInfer-Grafit repositories - Sections 1294 and 1302 - obstacles in lattice have been marked based on LiDAR data):
               while destination not reached:
               {