Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Mass spectrometry and n-in-one analytics in early drug discovery: Combinatorial chemistry libraries, lipophilicity and absorption screening

This thesis describes current and past n-in-one methods and presents three early experimental studies using mass spectrometry and the triple quadrupole instrument on the application of n-in-one in drug discovery. N-in-one strategy pools and mix samples in drug discovery prior to measurement or analysis. This allows the most promising compounds to be rapidly identified and then analysed. Nowadays properties of drugs are characterised earlier and in parallel with pharmacological efficacy. Studies presented here use in vitro methods as caco-2 cells and immobilized artificial membrane chromatography for drug absorption and lipophilicity measurements. The high sensitivity and selectivity of liquid chromatography mass spectrometry are especially important for new analytical methods using n-in-one. In the first study, the fragmentation patterns of ten nitrophenoxy benzoate compounds, serial homology, were characterised and the presence of the compounds was determined in a combinatorial library. The influence of one or two nitro substituents and the alkyl chain length of methyl to pentyl on collision-induced fragmentation was studied, and interesting structurefragmentation relationships were detected. Two nitro group compounds increased fragmentation compared to one nitro group, whereas less fragmentation was noted in molecules with a longer alkyl chain. The most abundant product ions were nitrophenoxy ions, which were also tested in the precursor ion screening of the combinatorial library. In the second study, the immobilized artificial membrane chromatographic method was transferred from ultraviolet detection to mass spectrometric analysis and a new method was developed. Mass spectra were scanned and the chromatographic retention of compounds was analysed using extract ion chromatograms. When changing detectors and buffers and including n-in-one in the method, the results showed good correlation. Finally, the results demonstrated that mass spectrometric detection with gradient elution can provide a rapid and convenient n-in-one method for ranking the lipophilic properties of several structurally diverse compounds simultaneously. In the final study, a new method was developed for caco-2 samples. Compounds were separated by liquid chromatography and quantified by selected reaction monitoring using mass spectrometry. This method was used for caco-2 samples, where absorption of ten chemically and physiologically different compounds was screened using both single and nin- one approaches. These three studies used mass spectrometry for compound identification, method transfer and quantitation in the area of mixture analysis. Different mass spectrometric scanning modes for the triple quadrupole instrument were used in each method. Early drug discovery with n-in-one is area where mass spectrometric analysis, its possibilities and proper use, is especially important.

Optimisation problems in wireless sensor networks

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.