# Algorithm Design Kleinberg Exercise Solutions

Algorithm Design introduces algorithms by looking at the real-world problems that motivate them. The book teaches students a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science. August 6, 2009 Author, Jon Kleinberg, was recently cited in the New York Times for his statistical analysis research in the Internet age.ExploreSimilar booksBook lists with this bookWhy do people like this book?TopicsComputer scienceDesignAlgorithmsGenresComing soon...PreviewBookshop.orgAmazonAlgorithms Illuminated (Part 1)ByTim Roughgarden,

## Algorithm Design Kleinberg Exercise Solutions

The authors' treatment of data structures in Data Structures and Algorithms is unified by an informal notion of "abstract data types," allowing readers to compare different implementations of the same concept. Algorithm design techniques are also stressed and basic algorithm analysis is covered. Most of the programs are written in Pascal.ExploreSimilar booksBook lists with this bookWhy do people like this book?TopicsAlgorithmsGenresComing soon...PreviewBookshop.orgAmazonA Common-Sense Guide to Data Structures and AlgorithmsByJay Wengrow,

------------------------MM: Algorithm design------------------------The aim of the course is to provide the student with the necessary skills and know-how for the design and analysis of algorithmic solutions to fundamental bioinformatics problems. This module focuses on general principles of advanced algorithm design, using examples taken from classical solutions of real-life bioinformatics problems. Within the overall goals of the Masters Course, the module Algorithm Design will provide the students with: a wealth of advanced techniques for tackling nontrivial problems in bioinformatics; the skill to design algorithmic solutions for typical problems in genome analysis; the ability to identify the structural elements that make a problem difficult or a solution inefficient; and the capability to propose appropriate approaches to the solution of hard problems in bioinformatics ------------------------MM: Bioinformatics algorithms------------------------To learn about some of the basic algorithmic problems and solutions behind common bioinformatics applications (sequence alignment, sequence similarity, sequence assembly, RNA folding).

------------------------MM: Algorithm design------------------------Fundamental notions of algorithmic analysis (brief recap): graph traversals; shortest paths in graphs; minimum spanning tree; dynamic programming. Elements of computational complexity and NP-completeness Models of Genome Rearrangement: (i) polynomial time algorithm for sorting signed permutations; (ii) approximation algorithms for sorting unsigned permutations; (iii) Synteny Distance Some Fundamental Graph Problems: (i) Graph tours: Hamiltonian Cycles and Eulerian Cycles; efficient algorithms for Eulerian path and Eulerian cycle; (ii) The Traveling Salesman Problem: relationships to the hamiltonian cycle problems; inapproximability of the symmetric TSP; 2 approximation algorithm for the metric TSP Models for Physical Map: (i) polynomial time algorithm for The Consecutive Ones Property (C1P); (ii) approximation algorithm for the gap minimisation based on the metric TSP Models for DNA assembly: The Shortest Common Superstring problem and the approximation of the the maximum compression via weighted matching. Network Flow: maximum flow and min cut problems; maximum matching; decomposition of flow into edge disjoint paths; polynomial time algorithm for the minimum/maximum weight perfect matching in bipartite graphs. Models for Motif Finding: (i) the Consensus String Problem; (ii) Polynomial Time Approximation Scheme. Models of Haplotyping: polynomial time algorithms for the haplotyping problem for single individual on gapless data; extensions and parameterisations in the presence of data with gaps.------------------------MM: Bioinformatics algorithms------------------------Here is an overview of the topics that will be covered. * Introduction Part I: Pairwise Sequence Comparison * Pairwise sequence alignment * String distances * Pairwise alignment in practice: BLAST, Scoring matrices Part II: Multiple sequence alignment * exact DP algorithm * Carillo-Lipman search space reduction * approximation algorithm, heuristics Part III: RNA folding * Nussinov and Zuker algorithms, * approximation algorithm Part IV: Sequence assembly algorithms * Shotgun sequencing: SCS and other models * Sequencing by Hybridization and NGS: de Bruijn graphs, Euler tours

------------------------MM: Algorithm design------------------------The exam verifies that the students can master the fundamental tools and techniques for the analysis and design of algorithms and that they understand how these techniques are employed in the solution of some classical computational problems arising in bioinformatics. The exam consists of a written test with open questions. The test includes some mandatory exercises and a set of exercises among which the student can choose what to work on. The mandatory exercises are meant to evaluate the student's knowledge of classical algorithms and analysis tools as seen during the course. "Free-choice" exercises test the ability of students to model "new" toy problems and design and analyse algorithmic solutions for it. The grade for the module Algorithm Design is determined by the result of the written test and the result of homework to be solved periodically during the semester. The overall grade for "Fundamental Algorithms for Bioinformatics" is computed by averaging the grades awarded for the two modules. ------------------------MM: Bioinformatics algorithms------------------------Written exam, followed by oral exam. You are only admitted to the oral if you have passed the written exam. The written exam consists of theoretical questions (problems studied, analysis of algorithms studied, mathematical properties, which algorithms exist for a problem etc.), as well as applications of algorithms to concrete examples (computing a pairwise alignment with the DP algorithm etc.) In the oral exam, the student will explain in detail their solutions to the written exam, and show to what extent they have mastered the topics. Students of the Masters in Molecular and medical biotechnology will have separate exams.

Collaboration policy for mandatory exercises You may collaborate in groups of up to 3 students on the mandatory exercises. The collaborators must be listed in your solution (see template).

Collaboration is limited to discussion of ideas only, and you should write up the solutions entirely on your own.

Do not use or seek out solutions from previous years of the course, solutions from similar courses, or solutions found on the internet.

In the last two decades, we have experienced an unprecedented growth in the area of distributed systems and networks; distributed computing now encompasses many of the activities occurring in today's computer and communications world. This course introduces the basics of distributed computing, highlighting common themes and techniques. We study the fundamental issues underlying the design of distributed systems: communication, coordination, synchronization, uncertainty. We explore essential algorithmic ideas and lower bound techniques.