Algorithmic Advancements and Massive Parallelism for Large-Scale Datasets in Phylogenetic Bayesian Markov Chain Monte Carlo

Datasets used for the inference of the "tree of life" grow at unprecedented rates, thus inducing a high computational burden for analytic methods. First, we introduce a scalable software package that allows us to conduct state of the art Bayesian analyses on datasets of almost arbitrary size. Second, we derive a proposal mechanism for MCMC that is substantially more efficient than traditional branch length proposals. Third, we present an efficient algorithm for solving the rogue taxon problem

New Algorithms andMethodology for Analysing Distances

Distances arise in a wide variety of di�erent contexts, one of which is partitional clustering, that is, the problem of �nding groups of similar objects within a set of objects.¿ese groups are seemingly very easy to �nd for humans, but very di�cult to �nd for machines as there are two major di�culties to be overcome: the �rst de�ning an objective criterion for the vague notion of “groups of similar objects”, and the second is the computational complexity of �nding such groups given a criterion. In the �rst part of this thesis, we focus on the �rst di�culty and show that even seemingly similar optimisation criteria used for partitional clustering can produce vastly di�erent results. In the process of showing this we develop a new metric for comparing clustering solutions called the assignment metric. We then prove some new NP-completeness results for problems using two related “sum-of-squares” clustering criteria. Closely related to partitional clustering is the problem of hierarchical clustering. We extend and formalise this problem to the problem of constructing rooted edge-weighted X-trees, that is trees with a leafset X. It is well known that an X-tree can be uniquely reconstructed from a distance on X if the distance is an ultrametric. But in practice the complete distance on X may not always be available. In the second part of this thesis we look at some of the circumstances under which a tree can be uniquely reconstructed from incomplete distance information. We use a concept called a lasso and give some theoretical properties of a special type of lasso. We then develop an algorithm which can construct a tree together with a lasso from partial distance information and show how this can be applied to various incomplete datasets

Constructing minimal cost/minimal SRLG spanning trees Over optical networks - An exact approach

The construction of overlay or broadcast networks, based on spanning trees, over WDM optical networks with SRLG information has important applications in telecommunications. In this paper we propose a bicriteria optimisation model for calculating communication spanning trees over WDM networks the objectives of which are the minimisation of the total number of different SRLGs of the tree links (seeking to maximise reliability) and the minimisation of the total bandwidth usage cost. An exact algorithm for generating the whole set of non-dominated solutions and methods for selecting a final solution in various decision environments, are put forward. An extensive experimental study on the application of the model, including two sets of experiments based on reference transport network topologies, with random link bandwidth occupations and with random SRLG assignments to the links, is also presented, together with a discussion on potential advantages of the model

Time/cost trade-offs in machine scheduling with controllable processing times

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 166-175Processing time controllability is a critical aspect in scheduling decisions since most of the scheduling practice in industry allows controlling processing times. A very well known example is the computer numerically controlled (CNC) machines in flexible manufacturing systems. Selected processing times for a given set of jobs determine the manufacturing cost of the jobs and strongly affect their scheduling performance. Hence, when making processing time and scheduling decisions at the same time, one must consider both the manufacturing cost and the scheduling performance objectives. In this thesis, we have studied such bicriteria scheduling problems in various scheduling environments including single, parallel and non-identical parallel machine environments. We have included some regular scheduling performance measures such as total weighted completion time and makespan. We have considered the convex manufacturing cost function of CNC turning operation. We have provided alternative methods to find efficient solutions in each problem. We have particularly focused on the single objective problems to get efficient solutions, called the -constraint approach. We have provided efficient formulations for the problems and shown useful properties which led us to develop fast heuristics to generate set of efficient solutions. In this thesis, taking another point of view, we have also studied a conic quadratic reformulation of a machine-job assignment problem with controllable processing times. We have considered a convex compression cost function for each job and solved a profit maximization problem. The convexity of cost functions is a major source of difficulty in finding optimal integer solutions in this problem, but our strengthened conic reformulation has eliminated this difficulty. Our reformulation approach is sufficiently general so that it can also be applied to other mixed 0-1 optimization problems with separable convex cost functions.Our computational results demonstrate that the proposed conic reformulation is very effective for solving the machine-job assignment problem with controllable processing times to optimality. Finally, in this thesis, we have considered rescheduling with controllable processing times. In particular, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules in response to a disruption such as machine breakdown. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain cost which is a convex function of the compression on the processing time. When rescheduling, it is critical to catch up the initial schedule as soon as possible by reassigning the jobs to the machines and changing their processing times. On the other hand, one must keep the total cost of the jobs at minimum. We present alternative match-up scheduling problems dealing with this trade-off. We use the strong conic reformulation approach in solving these problems. We further provide fast heuristic algorithms.Gürel, SinanPh.D