Searching a Tree with Permanently Noisy Advice

We consider a search problem on trees using unreliable guiding instructions. Specifically, an agent starts a search at the root of a tree aiming to find a treasure hidden at one of the nodes by an adversary. Each visited node holds information, called advice, regarding the most promising neighbor to continue the search. However, the memory holding this information may be unreliable. Modeling this scenario, we focus on a probabilistic setting. That is, the advice at a node is a pointer to one of its neighbors. With probability q each node is faulty, independently of other nodes, in which case its advice points at an arbitrary neighbor, chosen uniformly at random. Otherwise, the node is sound and points at the correct neighbor. Crucially, the advice is permanent, in the sense that querying a node several times would yield the same answer. We evaluate efficiency by two measures: The move complexity denotes the expected number of edge traversals, and the query complexity denotes the expected number of queries. Let Delta denote the maximal degree. Roughly speaking, the main message of this paper is that a phase transition occurs when the noise parameter q is roughly 1/sqrt{Delta}. More precisely, we prove that above the threshold, every search algorithm has query complexity (and move complexity) which is both exponential in the depth d of the treasure and polynomial in the number of nodes n. Conversely, below the threshold, there exists an algorithm with move complexity O(d sqrt{Delta}), and an algorithm with query complexity O(sqrt{Delta}log Delta log^2 n). Moreover, for the case of regular trees, we obtain an algorithm with query complexity O(sqrt{Delta}log n log log n). For q that is below but close to the threshold, the bound for the move complexity is tight, and the bounds for the query complexity are not far from the lower bound of Omega(sqrt{Delta}log_Delta n). In addition, we also consider a semi-adversarial variant, in which an adversary chooses the direction of advice at faulty nodes. For this variant, the threshold for efficient moving algorithms happens when the noise parameter is roughly 1/Delta. Above this threshold a simple protocol that follows each advice with a fixed probability already achieves optimal move complexity

Search for an Immobile Hider on a Stochastic Network

Harry hides on an edge of a graph and does not move from there. Sally, starting from a known origin, tries to find him as soon as she can. Harry's goal is to be found as late as possible. At any given time, each edge of the graph is either active or inactive, independently of the other edges, with a known probability of being active. This situation can be modeled as a zero-sum two-person stochastic game. We show that the game has a value and we provide upper and lower bounds for this value. Finally, by generalizing optimal strategies of the deterministic case, we provide more refined results for trees and Eulerian graphs.Comment: 28 pages, 9 figure

Binary search in graphs revisited

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by Emamjomeh-Zadeh et al. (in: Proceedings of the 48th annual ACM SIGACT symposium on theory of computing, STOC 2016, Cambridge, pp. 519–532, 2016) to the problem of detecting a target in an arbitrary graph. Similarly to the classical case in the path, the algorithm of Emamjomeh-Zadeh et al. maintains a candidates’ set for the target, while each query asks an appropriately chosen vertex—the “median”—which minimises a potential Φ among the vertices of the candidates’ set. In this paper we address three open questions posed by Emamjomeh-Zadeh et al., namely (a) detecting a target when the query response is a direction to an approximately shortest path to the target, (b) detecting a target when querying a vertex that is an approximate median of the current candidates’ set (instead of an exact one), and (c) detecting multiple targets, for which to the best of our knowledge no progress has been made so far. We resolve questions (a) and (b) by providing appropriate upper and lower bounds, as well as a new potential Γ that guarantees efficient target detection even by querying an approximate median each time. With respect to (c), we initiate a systematic study for detecting two targets in graphs and we identify sufficient conditions on the queries that allow for strong (linear) lower bounds and strong (polylogarithmic) upper bounds for the number of queries. All of our positive results can be derived using our new potential Γ that allows querying approximate medians

AI-Based Diagnostic Shell

This paper datails the design and implementation of an AI-based diagnostic shell. The shell has a user-interface which takes in the complaint and aids the user throughout the consultation. The 'expert knowledge' is acquired and encoded in the form of 'IF-THEN' rules, The control mechanism routes through the rules chaining first backwards to identify a fault and then forwards to confirm it.Explanation facilities have been provided to enable the user query the reason for any question asked, a facility to go back and re-answer any previous question, and a trace and explanation of the path of reasoning.This shell was developed and first used for the diagnosis of a digital exchange. It was then applied for the fault-finding of the moving target indicator used in the radar

FLAG : the fault-line analytic graph and fingerprint classification

Fingerprints can be classified into millions of groups by quantitative measurements of their new representations - Fault-Line Analytic Graphs (FLAG), which describe the relationship between ridge flows and singular points. This new model is highly mathematical, therefore, human interpretation can be reduced to a minimum and the time of identification can be significantly reduced. There are some well known features on fingerprints such as singular points, cores and deltas, which are global features which characterize the fingerprint pattern class, and minutiae which are the local features which characterize an individual fingerprint image. Singular points are more important than minutiae when classifying fingerprints because the geometric relationship among the singular points decide the type of fingerprints. When the number of fingerprint records becomes large, the current methods need to compare a large number of fingerprint candidates to identify a given fingerprint. This is the result of having a few synthetic types to classify a database with millions of fingerprints. It has been difficult to enlarge the minter of classification groups because there was no computational method to systematically describe the geometric relationship among singular points and ridge flows. In order to define a more efficient classification method, this dissertation also provides a systematic approach to detect singular points with almost pinpoint precision of 2x2 pixels using efficient algorithms