Wireless network applications, such as, searching, routing, self stabilization and query processing can be modeled as random walks on graphs. Stateless Opportunistic routing technique is a robust distributed routing technique based on random walk approach , where nodes transfer the packets to one of their direct neighbors uniformly, until the packets reach their destinations. Simplicity in exec...

Nearest neighbor searching is an important geometric subproblem in vector quanti-zation. Existing studies have shown that the diiculty of solving this problem eeciently grows rapidly with dimension. Indeed, existing approaches on unstructured codebooks in dimension 16 are little better than brute-force search. We show that if one is willing to relax the requirement of nding the true nearest nei...

In nearest neighbor searching we are given a set of n data points in real d-dimensional space, <d, and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported efficiently. Because data sets can be quite large, we are interested in data structures that use optimal O(dn) storage. In this paper we consi...

We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in R indexed by time such that we can perform insertions or deletions at any point in the timeline in O(log n) amortized time. We support, for any small constant > 0, (1 + )-approximate range rep...

We study the aggregate nearest neighbor searching for the Max operator in the plane. For a set P of n points and a query set Q of m points, the query asks for a point of P whose maximum distance to the points in Q is minimized. We present data structures for answering such queries for both L1 and L2 distance measures. Previously, only heuristic and approximation algorithms were given for both v...

Nearest neighbor searching is an important geometric subproblem in vector quantization. Existing studies have shown that the difficulty of solving this problem efficiently grows rapidly with dimension. Indeed, existing approaches on unstructured codebooks in dimension 16 are little better than brute-force search. We show that if one is willing to relax the requirement of finding the true neares...

This paper discusses a genetic-algorithm-based approach for selecting a small number of representative instances from a given data set in a pattern classification problem. The genetic algorithm also selects a small number of significant features. That is, instances and features are simultaneously selected for finding a compact data set. The selected instances and features are used as a referenc...

This thesis describes the implementation of a fast, dynamic, approximate, nearestneighbor search algorithm that works well in fixed dimensions (d ≤ 5), based on sorting points in Morton (or z-) ordering. This algorithm scales well on multi-core/cpu shared memory systems, and can run on multiple processors simultaneously. The implementation is competitive with the best approximate nearest neighb...

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P . Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P . All distances are measured using the geodesic distance, that is, the length of the shortest path...

The nearest neighbor problem is that of preprocessing a set P of n data points in Rd so that, given any query point q, the closest point in P to q can be determined efficiently. In the chromatic nearest neighbor problem, each point of P is assigned a color, and the problem is to determine the color of the nearest point to the query point. More generally, given k ≥ 1, the problem is to determine...