745 research outputs found
Reverse k Nearest Neighbor Search over Trajectories
GPS enables mobile devices to continuously provide new opportunities to
improve our daily lives. For example, the data collected in applications
created by Uber or Public Transport Authorities can be used to plan
transportation routes, estimate capacities, and proactively identify low
coverage areas. In this paper, we study a new kind of query-Reverse k Nearest
Neighbor Search over Trajectories (RkNNT), which can be used for route planning
and capacity estimation. Given a set of existing routes DR, a set of passenger
transitions DT, and a query route Q, a RkNNT query returns all transitions that
take Q as one of its k nearest travel routes. To solve the problem, we first
develop an index to handle dynamic trajectory updates, so that the most
up-to-date transition data are available for answering a RkNNT query. Then we
introduce a filter refinement framework for processing RkNNT queries using the
proposed indexes. Next, we show how to use RkNNT to solve the optimal route
planning problem MaxRkNNT (MinRkNNT), which is to search for the optimal route
from a start location to an end location that could attract the maximum (or
minimum) number of passengers based on a pre-defined travel distance threshold.
Experiments on real datasets demonstrate the efficiency and scalability of our
approaches. To the best of our best knowledge, this is the first work to study
the RkNNT problem for route planning.Comment: 12 page
CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries
The reverse nearest neighbor (RNN) query finds all points that have
the query point as one of their nearest neighbors (NN), where the NN
query finds the closest points to its query point. Based on the
characteristics of conic section, we propose a discriminance, named CSD (Conic
Section Discriminance), to determine points whether belong to the RNN set
without issuing any queries with non-constant computational complexity. By
using CSD, we also implement an efficient RNN algorithm CSD-RNN with a
computational complexity at . The comparative
experiments are conducted between CSD-RNN and other two state-of-the-art
RkNN algorithms, SLICE and VR-RNN. The experimental results indicate that
the efficiency of CSD-RNN is significantly higher than its competitors
Fine-Grained Complexity Analysis of Two Classic TSP Variants
We analyze two classic variants of the Traveling Salesman Problem using the
toolkit of fine-grained complexity. Our first set of results is motivated by
the Bitonic TSP problem: given a set of points in the plane, compute a
shortest tour consisting of two monotone chains. It is a classic
dynamic-programming exercise to solve this problem in time. While the
near-quadratic dependency of similar dynamic programs for Longest Common
Subsequence and Discrete Frechet Distance has recently been proven to be
essentially optimal under the Strong Exponential Time Hypothesis, we show that
bitonic tours can be found in subquadratic time. More precisely, we present an
algorithm that solves bitonic TSP in time and its bottleneck
version in time. Our second set of results concerns the popular
-OPT heuristic for TSP in the graph setting. More precisely, we study the
-OPT decision problem, which asks whether a given tour can be improved by a
-OPT move that replaces edges in the tour by new edges. A simple
algorithm solves -OPT in time for fixed . For 2-OPT, this is
easily seen to be optimal. For we prove that an algorithm with a runtime
of the form exists if and only if All-Pairs
Shortest Paths in weighted digraphs has such an algorithm. The results for
may suggest that the actual time complexity of -OPT is
. We show that this is not the case, by presenting an algorithm
that finds the best -move in time for
fixed . This implies that 4-OPT can be solved in time,
matching the best-known algorithm for 3-OPT. Finally, we show how to beat the
quadratic barrier for in two important settings, namely for points in the
plane and when we want to solve 2-OPT repeatedly.Comment: Extended abstract appears in the Proceedings of the 43rd
International Colloquium on Automata, Languages, and Programming (ICALP 2016
Algorithms for Stable Matching and Clustering in a Grid
We study a discrete version of a geometric stable marriage problem originally
proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which
points in the plane are stably matched to cluster centers, as prioritized by
their distances, so that each cluster center is apportioned a set of points of
equal area. We show that, for a discretization of the problem to an
grid of pixels with centers, the problem can be solved in time , and we experiment with two slower but more practical algorithms and
a hybrid method that switches from one of these algorithms to the other to gain
greater efficiency than either algorithm alone. We also show how to combine
geometric stable matchings with a -means clustering algorithm, so as to
provide a geometric political-districting algorithm that views distance in
economic terms, and we experiment with weighted versions of stable -means in
order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th
International Workshop on Combinatorial Image Analysis, June 19-21, 2017,
Plovdiv, Bulgari
Measuring Galaxy Environments with Deep Redshift Surveys
We study the applicability of several galaxy environment measures
(n^th-nearest-neighbor distance, counts in an aperture, and Voronoi volume)
within deep redshift surveys. Mock galaxy catalogs are employed to mimic
representative photometric and spectroscopic surveys at high redshift (z ~ 1).
We investigate the effects of survey edges, redshift precision, redshift-space
distortions, and target selection upon each environment measure. We find that
even optimistic photometric redshift errors (\sigma_z = 0.02) smear out the
line-of-sight galaxy distribution irretrievably on small scales; this
significantly limits the application of photometric redshift surveys to
environment studies. Edges and holes in a survey field dramatically affect the
estimation of environment, with the impact of edge effects depending upon the
adopted environment measure. These edge effects considerably limit the
usefulness of smaller survey fields (e.g. the GOODS fields) for studies of
galaxy environment. In even the poorest groups and clusters, redshift-space
distortions limit the effectiveness of each environment statistic; measuring
density in projection (e.g. using counts in a cylindrical aperture or a
projected n^th-nearest-neighbor distance measure) significantly improves the
accuracy of measures in such over-dense environments. For the DEEP2 Galaxy
Redshift Survey, we conclude that among the environment estimators tested the
projected n^th-nearest-neighbor distance measure provides the most accurate
estimate of local galaxy density over a continuous and broad range of scales.Comment: 17 pages including 16 figures, accepted to Ap
Boundary-Sensitive Approach for Approximate Nearest-Neighbor Classification
The problem of nearest-neighbor classification is a fundamental technique in machine-learning. Given a training set P of n labeled points in ?^d, and an approximation parameter 0 < ? ? 1/2, any unlabeled query point should be classified with the class of any of its ?-approximate nearest-neighbors in P. Answering these queries efficiently has been the focus of extensive research, proposing techniques that are mainly tailored towards resolving the more general problem of ?-approximate nearest-neighbor search. While the latest can only hope to provide query time and space complexities dependent on n, the problem of nearest-neighbor classification accepts other parameters more suitable to its analysis. Such is the number k_? of ?-border points, which describes the complexity of boundaries between sets of points of different classes.
This paper presents a new data structure called Chromatic AVD. This is the first approach for ?-approximate nearest-neighbor classification whose space and query time complexities are only dependent on ?, k_? and d, while being independent on both n and ?, the spread of P
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