Labeled Nearest Neighbor Search and Metric Spanners via Locality Sensitive Orderings

Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO) for Euclidean space. A $(\tau,\rho)$-LSO is a collection $\Sigma$ of orderings such that for every $x,y\in\mathbb{R}^d$ there is an ordering $\sigma\in\Sigma$, where all the points between $x$ and $y$ w.r.t. $\sigma$ are in the $\rho$-neighborhood of either $x$ or $y$. In essence, LSO allow one to reduce problems to the $1$-dimensional line. Later, Filtser and Le [STOC 2022] developed LSO's for doubling metrics, general metric spaces, and minor free graphs. For Euclidean and doubling spaces, the number of orderings in the LSO is exponential in the dimension, which made them mainly useful for the low dimensional regime. In this paper, we develop new LSO's for Euclidean, $\ell_p$, and doubling spaces that allow us to trade larger stretch for a much smaller number of orderings. We then use our new LSO's (as well as the previous ones) to construct path reporting low hop spanners, fault tolerant spanners, reliable spanners, and light spanners for different metric spaces. While many nearest neighbor search (NNS) data structures were constructed for metric spaces with implicit distance representations (where the distance between two metric points can be computed using their names, e.g. Euclidean space), for other spaces almost nothing is known. In this paper we initiate the study of the labeled NNS problem, where one is allowed to artificially assign labels (short names) to metric points. We use LSO's to construct efficient labeled NNS data structures in this model

Reasoning & Querying – State of the Art

Various query languages for Web and Semantic Web data, both for practical use and as an area of research in the scientific community, have emerged in recent years. At the same time, the broad adoption of the internet where keyword search is used in many applications, e.g. search engines, has familiarized casual users with using keyword queries to retrieve information on the internet. Unlike this easy-to-use querying, traditional query languages require knowledge of the language itself as well as of the data to be queried. Keyword-based query languages for XML and RDF bridge the gap between the two, aiming at enabling simple querying of semi-structured data, which is relevant e.g. in the context of the emerging Semantic Web. This article presents an overview of the field of keyword querying for XML and RDF

Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games

We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in NP ? coNP and not known to be in P. In a breakthrough result Calude, Jain, Khoussainov, Li, and Stephan constructed in 2017 a quasipolynomial time algorithm for solving parity games, which was quickly followed by a few other algorithms with the same complexity. Our objective is to investigate how these techniques can be extended to mean payoff games. The starting point is the combinatorial notion of universal trees: all quasipolynomial time algorithms for parity games have been shown to exploit universal trees. Universal graphs extend universal trees to arbitrary (positionally determined) objectives. We show that they yield a family of value iteration algorithms for solving mean payoff games which includes the value iteration algorithm due to Brim, Chaloupka, Doyen, Gentilini, and Raskin. The contribution of this paper is to prove tight bounds on the complexity of algorithms for mean payoff games using universal graphs. We consider two parameters: the largest weight N in absolute value and the number k of weights. The dependence in N in the existing value iteration algorithm is linear, we show that this can be improved to N^{1 - 1/n} and obtain a matching lower bound. However, we show that we cannot break the linear dependence in the exponent in the number k of weights implying that universal graphs do not yield a quasipolynomial time algorithm for solving mean payoff games

Enhancement of Query processing on XML data

Ph.DDOCTOR OF PHILOSOPH

Efficient Change Management of XML Documents

XML-based documents play a major role in modern information architectures and their corresponding work-flows. In this context, the ability to identify and represent differences between two versions of a document is essential. A second important aspect is the merging of document versions, which becomes crucial in parallel editing processes. Many different approaches exist that meet these challenges. Most rely on operational transformation or document annotation. In both approaches, the operations leading to changes are tracked, which requires corresponding editing applications. In the context of software development, however, a state-based approach is common. Here, document versions are compared and merged using external tools, called diff and patch. This allows users for freely editing documents without being tightened to special tools. Approaches exist that are able to compare XML documents. A corresponding merge capability is still not available. In this thesis, I present a comprehensive framework that allows for comparing and merging of XML documents using a state-based approach. Its design is based on an analysis of XML documents and their modification patterns. The heart of the framework is a context-oriented delta model. I present a diff algorithm that appears to be highly efficient in terms of speed and delta quality. The patch algorithm is able to merge document versions efficiently and reliably. The efficiency and the reliability of my approach are verified using a competitive test scenario

Building efficient wireless infrastructures for pervasive computing environments

Pervasive computing is an emerging concept that thoroughly brings computing devices and the consequent technology into people\u27s daily life and activities. Most of these computing devices are very small, sometimes even invisible , and often embedded into the objects surrounding people. In addition, these devices usually are not isolated, but networked with each other through wireless channels so that people can easily control and access them. In the architecture of pervasive computing systems, these small and networked computing devices form a wireless infrastructure layer to support various functionalities in the upper application layer.;In practical applications, the wireless infrastructure often plays a role of data provider in a query/reply model, i.e., applications issue a query requesting certain data and the underlying wireless infrastructure is responsible for replying to the query. This dissertation has focused on the most critical issue of efficiency in designing such a wireless infrastructure. In particular, our problem resides in two domains depending on different definitions of efficiency. The first definition is time efficiency, i.e., how quickly a query can be replied. Many applications, especially real-time applications, require prompt response to a query as the consequent operations may be affected by the prior delay. The second definition is energy efficiency which is extremely important for the pervasive computing devices powered by batteries. Above all, our design goal is to reply to a query from applications quickly and with low energy cost.;This dissertation has investigated two representative wireless infrastructures, sensor networks and RFID systems, both of which can serve applications with useful information about the environments. We have comprehensively explored various important and representative problems from both algorithmic and experimental perspectives including efficient network architecture design and efficient protocols for basic queries and complicated data mining queries. The major design challenges of achieving efficiency are the massive amount of data involved in a query and the extremely limited resources and capability each small device possesses. We have proposed novel and efficient solutions with intensive evaluation. Compared to the prior work, this dissertation has identified a few important new problems and the proposed solutions significantly improve the performance in terms of time efficiency and energy efficiency. Our work also provides referrable insights and appropriate methodology to other similar problems in the research community

Randomized approximation algorithms : facility location, phylogenetic networks, Nash equilibria

Despite a great effort, researchers are unable to find efficient algorithms for a number of natural computational problems. Typically, it is possible to emphasize the hardness of such problems by proving that they are at least as hard as a number of other problems. In the language of computational complexity it means proving that the problem is complete for a certain class of problems. For optimization problems, we may consider to relax the requirement of the outcome to be optimal and accept an approximate (i.e., close to optimal) solution. For many of the problems that are hard to solve optimally, it is actually possible to efficiently find close to optimal solutions. In this thesis, we study algorithms for computing such approximate solutions