Managing Time-Sensitive IoT Applications via Dynamic Application Task Distribution and Adaptation

The recent proliferation of the Internet of Things has led to the pervasion of networked IoT devices such as sensors, video cameras, mobile phones, and industrial machines. This has fueled the growth of Time-Sensitive IoT (TS-IoT) applications that must complete the tasks of (1) collecting sensor observations they need from appropriate IoT devices and (2) analyzing the data within application-specific time-bounds. If this is not achieved, the value of these applications and the results they produce depreciates. At present, TS-IoT applications are executed in a distributed IoT environment that consists of heterogeneous computing and networking resources. Due to the heterogeneous and volatile nature (e.g., unpredictable data rates and sudden disconnections) of the IoT environment, it has become a major challenge to ensure the time-bounds of TS-IoT applications. Many existing task management techniques (i.e., techniques that are used to manage the execution of IoT applications in distributed computing resources) that have been proposed to support TS-IoT applications to meet their time-bounds do not provide a sophisticated and complete solution to manage the TS-IoT applications in a manner in which their time-bounds are guaranteed. This paper proposes TIDA, a comprehensive platform for managing TS-IoT applications that includes a task management technique, called DTDA, which incorporates novel task sizing, distribution, and dynamic adaptation techniques. DTDA’s task sizing technique measures the computing resources required to complete each task of the TS-IoT application at hand in each available IoT device, edge computer (e.g., network gateways), and cloud virtual machine. DTDA’s task distribution technique distributes and executes the tasks of each TS-IoT application in a manner that their time-bound requirements are met. Finally, DTDA includes a task adaptation technique that dynamically adapts the distribution of tasks (i.e., redistributes TS-IoT application tasks) when it detects a potential application time-bound violation. The paper describes a proof-of-concept implementation of TIDA that uses Microsoft’s Orleans Actor Framework. Finally, the paper demonstrates that the DTDA task management technique of TIDA meets the time-bound requirements of TS-IoT applications by presenting an experimental evaluation involving real time-sensitive IoT applications from the smart city domain.

Improved Algorithms for Allen's Interval Algebra: a Dynamic Programming Approach

The constraint satisfaction problem (CSP) is an important framework in artificial intelligence used to model e.g. qualitative reasoning problems such as Allen's interval algebra A. There is strong practical incitement to solve CSPs as efficiently as possible, and the classical complexity of temporal CSPs, including A, is well understood. However, the situation is more dire with respect to running time bounds of the form O(f(n)) (where n is the number of variables) where existing results gives a best theoretical upper bound 2^O(n * log n) which leaves a significant gap to the best (conditional) lower bound 2^o(n). In this paper we narrow this gap by presenting two novel algorithms for temporal CSPs based on dynamic programming. The first algorithm solves temporal CSPs limited to constraints of arity three in O(3^n) time, and we use this algorithm to solve A in O((1.5922n)^n) time. The second algorithm tackles A directly and solves it in O((1.0615n)^n), implying a remarkable improvement over existing methods since no previously published algorithm belongs to O((cn)^n) for any c. We also extend the latter algorithm to higher dimensions box algebras where we obtain the first explicit upper bound.

Reconstructing Words from Right-Bounded-Block Words

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely determine a word. We show that a word [Formula: see text] can be reconstructed from the number of occurrences of at most [Formula: see text] scattered factors of the form [Formula: see text], where [Formula: see text] is the number of occurrences of the letter [Formula: see text] in [Formula: see text]. Moreover, we generalise the result to alphabets of the form [Formula: see text] by showing that at most [Formula: see text] scattered factors suffices to reconstruct [Formula: see text]. Both results improve on the upper bounds known so far. Complexity time bounds on reconstruction algorithms are also considered here.

On Special k-Spectra, k-Locality, and Collapsing Prefix Normal Words

The domain of Combinatorics on Words, first introduced by Axel Thue in 1906, covers by now many subdomains. In this work we are investigating scattered factors as a representation of non-complete information and two measurements for words, namely the locality of a word and prefix normality, which have applications in pattern matching. In the first part of the thesis we investigate scattered factors: A word u is a scattered factor of w if u can be obtained from w by deleting some of its letters. That is, there exist the (potentially empty) words u1, u2, . . . , un, and v0,v1,...,vn such that u = u1u2 ̈ ̈ ̈un and w = v0u1v1u2v2 ̈ ̈ ̈unvn. First, we consider the set of length-k scattered factors of a given word w, called the k-spectrum of w and denoted by ScatFactk(w). We prove a series of properties of the sets ScatFactk(w) for binary weakly-0-balanced and, respectively, weakly-c-balanced words w, i.e., words over a two- letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has c occurrences more than the other. In particular, we consider the question which cardinalities n = | ScatFactk (w)| are obtainable, for a positive integer k, when w is either a weakly-0- balanced binary word of length 2k, or a weakly-c-balanced binary word of length 2k ́ c. Second, we investigate k-spectra that contain all possible words of length k, i.e., k-spectra of so called k-universal words. We present an algorithm deciding whether the k-spectra for given k of two words are equal or not, running in optimal time. Moreover, we present several results regarding k-universal words and extend this notion to circular universality that helps in investigating how the universality of repetitions of a given word can be determined. We conclude the part about scattered factors with results on the reconstruction problem of words from scattered factors that asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely determine a word. We show that a word w P {a, b} ̊ can be reconstructed from the number of occurrences of at most min(|w|a, |w|b) + 1 scattered factors of the form aib, where |w|a is the number of occurrences of the letter a in w. Moreover, we generalise the result to alphabets of the form {1, . . . , q} by showing that at most ∑q ́1 |w|i (q ́ i + 1) scattered factors suffices to reconstruct w. Both results i=1 improve on the upper bounds known so far. Complexity time bounds on reconstruction algorithms are also considered here. In the second part we consider patterns, i.e., words consisting of not only letters but also variables, and in particular their locality. A pattern is called k-local if on marking the pattern in a given order never more than k marked blocks occur. We start with the proof that determining the minimal k for a given pattern such that the pattern is k-local is NP- complete. Afterwards we present results on the behaviour of the locality of repetitions and palindromes. We end this part with the proof that the matching problem becomes also NP-hard if we do not consider a regular pattern - for which the matching problem is efficiently solvable - but repetitions of regular patterns. In the last part we investigate prefix normal words which are binary words in which each prefix has at least the same number of 1s as any factor of the same length. First introduced in 2011 by Fici and Lipták, the problem of determining the index (amount of equivalence classes for a given word length) of the prefix normal equivalence relation is still open. In this paper, we investigate two aspects of the problem, namely prefix normal palindromes and so-called collapsing words (extending the notion of critical words). We prove characterizations for both the palindromes and the collapsing words and show their connection. Based on this, we show that still open problems regarding prefix normal words can be split into certain subproblems.

An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture

We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $$d^{-o_d(1)}$$ d - o d ( 1 ) . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $$d^{-1/4}$$ d - 1 / 4 . Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain’s slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concave measures and better mixing time bounds for MCMC sampling algorithms on log-concave measures.