Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices" of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Parameterized Complexity

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

Invitation to fixed-parameter algorithms

In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.

/pdf/a-linear-time-algorithm-for-finding-tree-decompositions-of-4u8h6zpm0r.pdf

A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

An annotation of a string X over an alphabet Σ is a string Y having the same length as X, over an alphabet Γ. The pair (X, Y) can be viewed as a string over the alphabet Σ×Γ. The search problem for a language L ⊑ (Σ × Γ)* is the problem of computing, given a string X ∈ Σ*, a string Y ∈ Γ*, having the same length as X, such that (X, Y) ∈ L, or determining that no such Y exists. We define a notion of finitestate searchability and prove the following (main) theorem: If L is finitestate recognizable, then it is finitestate searchable. The notions of annotation and finite-state searchability can be generalized to trees of symbols. Annotation search problems have a variety of applications. For example, the tree or string of symbols may represent the structural parse of a graph of bounded treewidth or pathwidth, and the annotation may represent a “solution” to a search problem (e.g., finding a subgraph homeomorphic to a fixed graph H). Our main theorem allows us to treat in a general and natural way the search problems that correspond to the many important graph decision problems now known to be solvable in linear time for graphs of bounded treewidth and pathwidth. As a corollary, we show finite-state searchability for graph properties whose solutions can be expressed by leading existential quantification in monadic second-order logic. This can be viewed as a “search problem” form of Courcelle's Theorem on the decidability of monadic second-order graph properties. We describe several possible applications to computing annotations of biological sequences, and discuss how the resulting annotations may be useful in sequence comparison and alignment.

Finite-state computability of annotations of strings and trees (extended abstract)

Most input distributions encountered in real-world applications of computing have highly significant extra structure that is not treated appropriately when only the overall instance size n is considered in complexity analysis and algorithm design. Parameterized complexity unfolds from this empirical observation as essentially a two-dimensional generalization of the familiar one-dimensional framework of " P versus NP ". The first part of the talk will cover the basics of this relatively new framework that pits fixed-parameter tractability (FPT) as the two-dimensional analog of P, against the two-dimensional analog of NP-hardness, which is hardness for W [1]. In this framework, the first dimension (as before) is the overall input size n, and the second dimension (the parameter) k provides a way of including the extra structure into problem complexity analysis and algorithm design. Some structural parameters, such as bounded treewidth, turn out to be nearly universal in practical scope. The connection to extremal structure theory develops in the following way. One can show that a parameterized problem is in FPT if and only if an input instance (x, k) can be transformed in polynomial time (polynomial in both dimensions, n and k) into an " equivalent " instance (x , k) that satisfies: (1) (x , k) is a yes-instance if and only if (x, k) is a yes instance, (2) |x | ≤ g(k) for some function g(k), and (3) k ≤ k. In this way, FPT algorithm design inevitably generates the quite natural question of how powerful this data-reduction or problem kernelization can be. The transformation of (x, k) into the smaller equivalent instance (x , k) is essentially pre-processing in polynomial time, and as such is directly exportable to useful heuristics. (Powerful software packages for hard problems, such as CPLEX, often depend crucially on smart and muscular polynomial-time preprocessing.) In other words, we are interested in achieving g(k) as small as possible in polynomial time. Thus FPT leads inevitably to polynomial-time extremal structure theory. The talk is about a systematic approach to designing such extremal structure and kernel-ization algorithms. The history and recent achievements of this systematic approach will be surveyed, and the method will be illustrated by some new results on kernelization for the MAX LEAF SPANNING TREE problem.

FPT is P-Time Extremal Structure I (Fixed-parameter tractability is polynomial-time extremal structure theory)

The problem of counting spanning trees in regular multigraphs is considered. The emphasis is on the case of directed trees. It is shown that the numbers of spanning in-trees and out-trees with respect to any point of a regular multigraph are the same. A general formula for counting directed spanning trees with the use of graph eigenvalues is introduced. Formulae for computing eigenvalues of Cayley multigraphs are presented.

Counting spanning trees in directed regular multigraphs

Finite-State Computability of Annotations of Strings and Trees

Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for finding obstructions by using a bounded treewidth (or pathwidth) search. We illustrate this approach by characterizing certain families of cycle-cover graphs based on the two well-known problems: $k$-{\sc Feedback Vertex Set} and $k$-{\sc Feedback Edge Set}. Our search is based on a number of algorithmic strategies by which large constants can be mitigated, including a randomized strategy for obtaining proofs of minimality.

Michael R. Fellows

Papers

Finite-state computability of annotations of strings and trees (extended abstract)

FPT is P-Time Extremal Structure I (Fixed-parameter tractability is polynomial-time extremal structure theory)

Counting spanning trees in directed regular multigraphs

Finite-State Computability of Annotations of Strings and Trees

Obstructions to within a few vertices or edges of acyclic