Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Phase Transition in the Aldous-Shields Model of Growing Trees

We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c^{-l} where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a `phase transition' at a critical value c=sqrt{2}. While for c>sqrt{2} the variance is proportional to the mean and the distribution is normal, for c<sqrt{2} the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with $m$ branches and, in this more general case, we show that the critical point occurs at c=sqrt{m}.Comment: Latex 17 pages, 6 figure

Positive Identification via Frontal Sinus Morphology: A Geographic Information Systems (GIS) Approach

Frontal sinus radiographs are frequently used to identify human remains. However, the method of visually comparing antemortem (AM) to postmortem (PM) cranial radiographs has been critiqued for its lack of sufficient error rates and the potential of practitioner training, experience, and education to influence results (Page, et al. 2011). In an effort to provide a more quantifiable method of frontal sinus identification, this thesis explored the use of the ArcGIS mapping software, ArcMap, and its spatial analyst tool, Similarity Search, for identifying frontal sinus matches. AM and PM cranial radiographs for 100 donors from the William M. Bass Donated Skeletal Collection and the Forensic Skeletal Collection at the University of Tennessee, Knoxville were organized into test groups containing one PM radiograph and ten AM radiographs and were uploaded into ArcMap 10.5 (ESRI 2018). Each frontal sinus was digitized using the Create Features tool, and the area and perimeter was calculated for the resulting polygons using the Calculate Geometry tool. For each test group, the Similarity Search tool was instructed to select the AM frontal sinus polygon that was most similar to the PM frontal sinus polygon based on the area and perimeter values. The percentage of correct matches by Similarity Search was calculated and statistical analyses were conducted to assess inter-observer and intra-observer variation, and to establish a threshold of similarity index values for correctly identified polygons. The results indicate that area and perimeter do not capture shape, only size. Based on these results it is concluded that for this method to be usable in forensic casework, more analyses will need to be included that provide Similarity Search with more characteristics than just area and perimeter and provide Similarity Search with information about the shape of the polygons

Selecting source image sensor nodes based on 2-hop information to improve image transmissions to mobile robot sinks in search \& rescue operations

We consider Robot-assisted Search $\&$ Rescue operations enhanced with some fixed image sensor nodes capable of capturing and sending visual information to a robot sink. In order to increase the performance of image transfer from image sensor nodes to the robot sinks we propose a 2-hop neighborhood information-based cover set selection to determine the most relevant image sensor nodes to activate. Then, in order to be consistent with our proposed approach, a multi-path extension of Greedy Perimeter Stateless Routing (called T-GPSR) wherein routing decisions are also based on 2-hop neighborhood information is proposed. Simulation results show that our proposal reduces packet losses, enabling fast packet delivery and higher visual quality of received images at the robot sink

Bidirectional Heuristic Search Reconsidered

The assessment of bidirectional heuristic search has been incorrect since it was first published more than a quarter of a century ago. For quite a long time, this search strategy did not achieve the expected results, and there was a major misunderstanding about the reasons behind it. Although there is still wide-spread belief that bidirectional heuristic search is afflicted by the problem of search frontiers passing each other, we demonstrate that this conjecture is wrong. Based on this finding, we present both a new generic approach to bidirectional heuristic search and a new approach to dynamically improving heuristic values that is feasible in bidirectional search only. These approaches are put into perspective with both the traditional and more recently proposed approaches in order to facilitate a better overall understanding. Empirical results of experiments with our new approaches show that bidirectional heuristic search can be performed very efficiently and also with limited memory. These results suggest that bidirectional heuristic search appears to be better for solving certain difficult problems than corresponding unidirectional search. This provides some evidence for the usefulness of a search strategy that was long neglected. In summary, we show that bidirectional heuristic search is viable and consequently propose that it be reconsidered.Comment: See http://www.jair.org/ for any accompanying file

Minimum Perimeter Rectangles That Enclose Congruent Non-Overlapping Circles

We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings found, the circles form the usual regular square-grid or hexagonal patterns or their hybrids. However, for most values of n in the tested range n =< 5000, e.g., for n = 7, 13, 17, 21, 22, 26, 31, 37, 38, 41, 43...,4997, 4998, 4999, 5000, we prove that the optimum cannot possibly be achieved by such regular arrangements. Usually, the irregularities in the best packings found for such n are small, localized modifications to regular patterns; those irregularities are usually easy to predict. Yet for some such irregular n, the best packings found show substantial, extended irregularities which we did not anticipate. In the range we explored carefully, the optimal packings were substantially irregular only for n of the form n = k(k+1)+1, k = 3, 4, 5, 6, 7, i.e., for n = 13, 21, 31, 43, and 57. Also, we prove that the height-to-width ratio of rectangles of minimum perimeter containing packings of n congruent circles tends to 1 as n tends to infinity.Comment: existence of irregular minimum perimeter packings for n not of the form (10) is conjectured; smallest such n is n=66; existence of irregular minimum area packings is conjectured, e.g. for n=453; locally optimal packings for the two minimization criteria are conjecturally the same (p.22, line 5); 27 pages, 12 figure

Quantum walks on two-dimensional grids with multiple marked locations

The running time of a quantum walk search algorithm depends on both the structure of the search space (graph) and the configuration of marked locations. While the first dependence have been studied in a number of papers, the second dependence remains mostly unstudied. We study search by quantum walks on two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. The original paper analyses one and two marked location cases only. We move beyond two marked locations and study the behaviour of the algorithm for an arbitrary configuration of marked locations. In this paper we prove two results showing the importance of how the marked locations are arranged. First, we present two placements of $k$ marked locations for which the number of steps of the algorithm differs by $\Omega(\sqrt{k})$ factor. Second, we present two configurations of $k$ and $\sqrt{k}$ marked locations having the same number of steps and probability to find a marked location

Image Processing Instrumentation for Giardia lamblia Detection

Currently, the identification and enumeration of Giardia Iamblia cysts are based upon microscopic methods requiring individuals proficient in this area. It is a tedious process which consumes time that could be constructively used elsewhere. This project attempts to alleviate that burden by employing a computer to automatically process Indirect Fluorescent Antibody (IFA) prepared slides using digital image processing techniques. A computer controlled frame grabber, in conjunction with a CCD TV camera mounted on the epi-fluorescence microscope phototube, captures the light intensities of the objects in view under the microscope objective. The captured image is stored as pixels, with each pixel having a numerical value that can be altered using linear contrast enhancement and bit-slicing to emphasize the cysts and eliminate the majority of unwanted objects from the image. The altered image is then analyzed by a vector trace routine for typical area and perimeters characteristic to Giardia lamblia cysts. Objects in the image matching these characteristics are most likely cysts and are added to a running tally of the number of cysts present on the slide