We consider the problem of fault-tolerant parallel search on an infinite line by @math robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed @math and can communicate in wireless mode among themselves. However, among the @math robots, there are @math robots that exhibit byzantine faults . A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of @math , the time to find a target at a distance @math from the origin by @math robots among which @math are faulty. We give several different algorithms whose running time depends on the ratio @math , the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.
In several studies, when the environment is not known in advance, search implies exploration, often involving mapping and localizing searchers within the environment @cite_17 @cite_5 @cite_30 @cite_15 @cite_20 @cite_18 . However, even for the case of a known, simple environment like a line, there were several interesting studies attempting to optimize the search time. They started with the independent works of Bellman @cite_29 and Beck @cite_6 , in which the authors attempted to minimize the competitive ratio in a stochastic setting. More exactly, they proved that time @math is needed to guarantee finding the target situated at a ( unknown) distance @math from the origin. Several other works on linear search followed (e.g. see @cite_9 @cite_6 @cite_23 @cite_16 @cite_24 @cite_26 @cite_29 ). More recently the search by a single searcher was studied for different models, e.g., when the turn cost was considered @cite_19 , when the bounds on the distance to the target are known in advance @cite_14 , and when the target was moving or for more general linear cost functions @cite_22 .
@cite_30 @cite_18 @cite_26 @cite_14 @cite_22 @cite_29 @cite_9 @cite_6 @cite_24 @cite_19 @cite_23 @cite_5 @cite_15 @cite_16 @cite_20 @cite_17
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The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9 ċ OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences for an explicit proof of optimality. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cowpath problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of (1 + 2mm (m - 1)m-1)OPT + m((m (m - 1))m-1 - 1)d. We also discuss tradeoffs between the corresponding coefficients and we consider randomized strategies on the line. In this paper, we present the results of a user study on exploratory search activities in a social science digital library. We conducted a user study with 32 participants with a social sciences background—16 postdoctoral researchers and 16 students—who were asked to solve a task on searching related work to a given topic. The exploratory search task was performed in a 10-min time slot. The use of certain search activities is measured and compared to gaze data recorded with an eye tracking device. We use a novel tree graph representation to visualise the users’ search patterns and introduce a way to combine multiple search session trees. The tree graph representation is capable of creating one single tree for multiple users and identifying common search patterns. In addition, the information behaviour of students and postdoctoral researchers is being compared. The results show that search activities on the stratagem level are frequently utilised by both user groups. The most heavily used search activities were keyword search, followed by browsing through references and citations, and author searching. The eye tracking results showed an intense examination of documents metadata, especially on the level of citations and references. When comparing the group of students and postdoctoral researchers, we found significant differences regarding gaze data on the area of the journal name of the seed document. In general, we found a tendency of the postdoctoral researchers to examine the metadata records more intensively with regard to dwell time and the number of fixations. By creating combined session trees and deriving subtrees from those, we were able to identify common patterns like economic (explorative) and exhaustive (navigational) behaviour. Our results show that participants utilised multiple search strategies starting from the seed document, which means that they examined different paths to find related publications. We consider the problem of searching on m current rays for a target of unknown location. If no upper bound on the distance to the target is known in advance, then the optimal competitive ratio is 1+2mm (m−1)m−1. We show that even if an upper bound of D on the distance to the target is known in advance, then the competitive ratio of any search strategy is at least 1+2mm (m−1)m−1−O(1 log2D). This is again optimal – but in a stricter sense. In particular, this result implies the same lower bound for a robot searching for a target on infinite rays and finding it at a distance of D. To show that our lower bound is, indeed, optimal we construct a search strategy that achieves this ratio. Our strategy does not need to know an upper bound on the distance to the target in advance; it achieves a competitive ratio of 1+2mm (m−1)m−1−O(1 log2D) if the target is found at distance D. Finally, we also present a linear time algorithm to compute the strategy that allows the robot to search the farthest for a given competitive ratio C.