Allocation problems have been central to the development of the theory of algorithms and also find applications in several realms of computer science and economics. In this thesis we initiate a systematic study of these problems in situations with limited information. Towards this end we explore several modes by which data may be obfuscated from the algorithm. We begin by investigating temporal constraints where data is revealed to the algorithm over time. Concretely, we consider the online bipartite matching problem in the unknown distribution model and present the first algorithm that breaches the 1-1/e barrier for this problem. Next we study issues arising from data acquisition costs that are prevalent in ad-systems and kidney exchanges. Motivated by these constraints we introduce the query-commit model and present constant factor algorithms for the maximum matching and the adwords problem in this model. Finally we assess the approximability of several classical allocation problems with multiple agents having complex non-linear cost functions. This presents an additional obstacle since the support for the cost functions may be extremely large entailing oracle access. We show tight information theoretic lower bounds for the general class of submodular functions and also extend these results to get lower bounds for a subclass of succinctly representable non-linear cost functions.

by Mei Long. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 93-98). / Abstracts in English and Chinese. / Table of Contents --- p.v / Abstract --- p.viii / Acknowledgements --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Satisfiability Problem --- p.1 / Chapter 1.2 --- Motivation of the Research --- p.1 / Chapter 1.3 --- Overview of the Thesis --- p.2 / Chapter 2 --- Satisfiability Problem --- p.4 / Chapter 2.1 --- Satisfiability Problem --- p.5 / Chapter 2.1.1 --- Basic Definition --- p.5 / Chapter 2.1.2 --- Phase Transitions --- p.5 / Chapter 2.2 --- History --- p.6 / Chapter 2.3 --- The Basic Search Algorithm --- p.8 / Chapter 2.4 --- Some Improvements to the Basic Algorithm --- p.9 / Chapter 2.4.1 --- Satz by Chu-Min Li --- p.9 / Chapter 2.4.2 --- Heuristics and Local Search --- p.12 / Chapter 2.4.3 --- Relaxation --- p.13 / Chapter 2.5 --- Benchmarks --- p.14 / Chapter 2.5.1 --- Specific Problems --- p.14 / Chapter 2.5.2 --- Randomly Generated Problems --- p.14 / Chapter 2.6 --- Software and Internet Information for SAT solving --- p.16 / Chapter 2.6.1 --- Stochastic Local Search Algorithms (incomplete) --- p.16 / Chapter 2.6.2 --- Systematic Search Algorithms (complete) --- p.16 / Chapter 2.6.3 --- Some useful Links to SAT Related Sites --- p.17 / Chapter 3 --- Integer Programming Formulation for Logic Problem --- p.18 / Chapter 3.1 --- SAT Problem --- p.19 / Chapter 3.2 --- MAXSAT Problem --- p.19 / Chapter 3.3 --- Logical Inference Problem --- p.19 / Chapter 3.4 --- Weighted Exact Satisfiability Problem --- p.20 / Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.22 / Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.22 / Chapter 4.2 --- Integer Programming Model for 3-SAT --- p.23 / Chapter 4.3 --- The Equivalence of the SAT and the IP --- p.23 / Chapter 4.4 --- Example --- p.24 / Chapter 5 --- Integer Solvability of Linear Programs --- p.27 / Chapter 5.1 --- Unimodularity --- p.27 / Chapter 5.2 --- Totally Unimodularity --- p.28 / Chapter 5.3 --- Some Results on Recognition of Linear Solvability of IP --- p.32 / Chapter 6 --- TU Based Matrix Research Results --- p.33 / Chapter 6.1 --- 2x2 Matrix's TU Property --- p.33 / Chapter 6.2 --- Extended Integer Programming Model for SAT --- p.34 / Chapter 6.3 --- 3x3 Matrix's TU Property --- p.35 / Chapter 7 --- Totally Unimodularity Based Branching-and-Bound Algorithm --- p.38 / Chapter 7.1 --- Introduction --- p.38 / Chapter 7.1.1 --- Enumeration Trees --- p.39 / Chapter 7.1.2 --- The Concept of Branch and Bound --- p.42 / Chapter 7.2 --- TU Based Branching Rule --- p.43 / Chapter 7.2.1 --- How to sort variables based on 2x2 submatrices --- p.43 / Chapter 7.2.2 --- How to sort the rest variables --- p.45 / Chapter 7.3 --- TU Based Bounding Rule --- p.46 / Chapter 7.4 --- TU Based Branch-and-Bound Algorithm --- p.47 / Chapter 7.5 --- Example --- p.49 / Chapter 8 --- Numerical Result --- p.57 / Chapter 8.1 --- Experimental Result --- p.57 / Chapter 8.2 --- Statistical Results of ILOG CPLEX --- p.59 / Chapter 9 --- Conclusions --- p.61 / Chapter 9.1 --- Contributions --- p.61 / Chapter 9.2 --- Future Work --- p.62 / Chapter A --- The Coefficient Matrix A for Example in Chapter 7 --- p.64 / Chapter B --- The Detailed Numerical Information of Solution Process for Exam- ple in Chapter 7 --- p.66 / Chapter C --- Experimental Result --- p.67 / Chapter C.1 --- "# of variables: 20, # of clauses: 91" --- p.67 / Chapter C.2 --- "# of variables: 50, # of clauses: 218" --- p.70 / Chapter C.3 --- # of variables: 75，# of clauses: 325 --- p.73 / Chapter C.4 --- "# of variables: 100, # of clauses: 430" --- p.76 / Chapter D --- Experimental Result of ILOG CPLEX --- p.80 / Chapter D.1 --- # of variables: 20´ة # of clauses: 91 --- p.80 / Chapter D.2 --- # of variables: 50，#of clauses: 218 --- p.83 / Chapter D.3 --- # of variables: 75，# of clauses: 325 --- p.86 / Chapter D.4 --- "# of variables: 100, # of clauses: 430" --- p.89 / Bibliography --- p.93

No description available.

The k-path problem is to find a simple path of length k. This problem is NP-complete and has applications in bioinformatics for detecting signaling pathways in protein interaction networks and for biological subnetwork matching. There are algorithms implemented to solve the problem for k up to 13. The fastest implementation has running time O^*(4.32^k), which is slower than the best known algorithm of running time O^*(4^k). To implement the best known algorithm for the k-path problem, we need to construct (n,k)-universal set. In this thesis, we study the practical algorithms for constructing the (n,k)-universal set problem. We propose six algorithm variants to handle the increasing computational time and memory space needed for k=3, 4, ..., 8. We propose two major empirical techniques that cut the time and space tremendously, yet generate good results. For the case k=7, the size of the universal set found by our algorithm is 1576, and is 4611 for the case k=8. We implement the proposed algorithms with the OpenMP parallel interface and construct universal sets for k=3, 4, ..., 8. Our experiments show that our algorithms for the (n,k)-universal set problem exhibit very good parallelism and hence shed light on its MPI implementation. Ours is the first implementation effort for the (n,k)-universal set problem. We share the effort by proposing an extensible universal set construction and retrieval system. This system integrates universal set construction algorithms and the universal sets constructed. The sets are stored in a centralized database and an interface is provided to access the database easily. The (n,k)-universal set have been applied to many other NP-complete problems such as the set splitting problems and the matching and packing problems. The small (n,k)-universal set constructed by us will reduce significantly the time to solve those problems.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 69-70). Also available in electronic version. Access restricted to campus users.

Recent research addresses the problem of data-stream mining to deal with applications that require processing huge amounts of data such as sensor data analysis and financial applications. Data-stream mining algorithms incorporate special provisions to meet the requirements of stream-management systems, that is stream algorithms must be online and incremental, processing each data record only once (or few times); adaptive to distribution changes; and fast enough to accommodate high arrival rates. We consider the problem of data-stream classification, introducing an online and incremental stream-classification ensemble algorithm, Streaming Random Forests, an extension of the Random Forests algorithm by Breiman, which is a standard classification algorithm. Our algorithm is designed to handle multi-class classification problems. It is able to deal with data streams having an evolving nature and a random arrival rate of training/test data records. The algorithm, in addition, automatically adjusts its parameters based on the data seen so far. Experimental results on real and synthetic data demonstrate that the algorithm gives a successful behavior. Without losing classification accuracy, our algorithm is able to handle multi-class problems for which the underlying class boundaries drift, and handle the case when blocks of training records are not big enough to build/update the classification model. / Thesis (Ph.D, Computing) -- Queen's University, 2008-07-15 16:12:33.221

We introduce two online models for the vertex k-center and the vertex k-median problems. Clients (i.e., graph vertices) and their corresponding links (i.e., graph edges) are revealed sequentially, determining the topology of a graph over time. Clients are revealed by an adversary to an online algorithm that selects existing graph vertices on which to open facilities; once open, a facility cannot be removed or relocated. We define two models: an online algorithm may be restricted to open a facility only at the location of the most recent client or at the location of any existing client. We examine these models on three classes of graphs under two types of adversaries. We establish lower bounds on the respective competitive ratios attainable by any online algorithm for each combination of model, adversary, and graph class. Finally, we describe algorithms whose competitive ratios provide corresponding upper bounds on the best competitive ratios achievable.

We introduce two online models for the vertex k-center and the vertex k-median problems. Clients (i.e., graph vertices) and their corresponding links (i.e., graph edges) are revealed sequentially, determining the topology of a graph over time. Clients are revealed by an adversary to an online algorithm that selects existing graph vertices on which to open facilities; once open, a facility cannot be removed or relocated. We define two models: an online algorithm may be restricted to open a facility only at the location of the most recent client or at the location of any existing client. We examine these models on three classes of graphs under two types of adversaries. We establish lower bounds on the respective competitive ratios attainable by any online algorithm for each combination of model, adversary, and graph class. Finally, we describe algorithms whose competitive ratios provide corresponding upper bounds on the best competitive ratios achievable.

Thesis (Ph.D.) -- University of Adelaide, School of Agriculture, Food and Wine, Discipline of Biometrics SA, 2008. / "October 2008" Includes bibliography (p. 283-290) Also available in print form.

Thesis (M.S.)--Rochester Institute of Technology, 1992. / Typescript. Includes bibliographical references (leaves 68-69).