CS091M4041H: Algorithm Design and Analysis  Fall 2015
Course Information

Staff
Instructor:
Dongbo Bu
Email: dbu AT ict.ac.cn
Location: Room 844, ICT Building,
Tel: 62600844
TAs:
Yaojun Wang,
Jianwei Zhu,
Feng Gao,
Yano Li,
Bing Wang,
Hai'e Gong,
Fei Yang,
Email: TA of alGorithm Courses
Location: 0817, ICT Building,
Tel: 62600887
Office Hours: 3:00pm6:00pm, Wednesday

Textbooks (recommended, not required):
* T.H. Cormen, C.E. Leiserson, R. Rivest, and C. Stein, Introduction to algorithms (2nd ed.), MIT Press, 2001. Widely available.
* J. Kleinberg and E. Tardos. Algorithm Design, AddisonWesley, 2005.
* R. Motwani and P. Raghavan, Randomized Algorithms. Cambridge U. Press, 1995
* Christos H. Papadimitriou, Kenneth Steiglitz, Kenneth Steiglitz.
Combinatorial Optimization: Algorithms And Complexity. Courier Dover Publications, 1998
* DingZhu Du, KerI Ko, Xiaodong Hu. Design and analysis of approximation algorithms. Springer, 2012
* Daming Zhu, Shaohan Ma. Algorithm design and analysis. High Education Press, 2009.
Other reading material:
* Udi Manber, Introduction to Algorithms: A Creative Approach.
* M. Mitzenmacher and E. Upfal, Probability and Computer. Cambridge U. Press, 2005.
* M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide
to the Theory of NPCompleteness. W.H. Freeman, New York, 1979.

Goals:
* to master the ability to extract mathematically clean core of a problem,
* then identify an appropriate algorithm design technique based on the problem structure observations,
* and analyze algorithm performance.

Prerequisites:
We will assume knowledge of:
* Basic data structures such as lists, trees, heaps, sorting and searching
* Basic discrete mathematics such as proofs by mathematical induction;
* Computability and programming experience;

Topics:
We will cover the following topics if time permits.
* Problem hardness, NPcompleteness;
* Algorithm analysis techniques, including worstcase and averagecase, amortized, randomization, and competitive;
* Basic algorithm techniques, including greedy, iteration,
divideandconquer, dynamic programming, network flow, linear
programming;
* Algorithm techniques for hard problems, including approximation
algorithms, local search, primaldual algorithms, linear programming;
* Randomized algorithms: basic techniques from discrete probability, and applications to optimization.
* Specific problems from computational biology and Bioinformatics (if time permits).
Grading policies
8 assignments and final examination.
Weekly Schedule
The week number is an active link  each week has its own page that
includes required reading, recommended reading, assignment (if any),
teaching assistants, etc. (Topics for weeks beyond the current and next
are always tentative.)
 Week 1,2,3: Introduction to algorithm and basic design techniques

Lecture 1: Introduction to algorithm: some representative problems;
Lec1.pdf ;

Lecture 3: Divideandconquer technique, and the combination with randomization;
Lec5.pdf ;
Lec5FFT.pdf ;
demo merge (by K. Wayne) ; demo merge inversion (by K. Wayne)
demo of QuickSort partition (by Y. Danial Liang) ;
 Reading material:
 Chapter 1 of Algorithm design,
 Chapter 17 of Introduction to Algorithms,
 Lecture 8, 9 of The Design and Analysis of Algorithms,
 On the solution of linear recurrence equations (by Mohamad Akra and Louay Bazzi, 1998) ,
 College Admissions and the Stability of Marriage (by Gale and Shapley, 1962) ,
 STABLE ALLOCATIONS AND THE PRACTICE OF MARKET DESIGN (compiled by the Economic Sciences Prize Committee of the Royal Swedish Academy of Sciences, 2012) ,
 Stable matching: Theory, evidence, and practical design (INFORMATION FOR THE PUBLIC, The Nobel prize in economic sciences, 2012) ,
 Who is Interested in Algorithms and Why? Lessons from the Stony Brook Algorithms Repository (by Steven S. Skiena, 1999) ,
 An Effective Heuristic Algorithm for the TravelingSalesman Problem (by S. Lin and B. W. Kernighan, 1971) ,
 Gene coexpression measures in large heterogeneous
samples using count statistics (by Y. Wang, M. S. Waterman, and H. Huang, 2014) ,
 Chapter 2,15,16,7,33.4 of Introduction to Algorithms,
 Chapter 5,4,6 of Algorithm design,
 Duality applied to the complexity of matrix multiplications and other bilinear forms (by J. Hopcroft, and J. Musinski, 1973) ,
 The CoppersmithWinograd matrix multiplication algorithm (by M. Anderson and S. Barman, 2009) ,
 Some techniques for solving recurrences (by George S. Lueker, 1980)
 Karatsuba algorithm vs. gradeschool method: experimental results (by Carl Burch)
 Fast Division of Large Integers  A comparison of Algorithms (by Karl Hasselstrom, 2003)
 Quicksort (by C. A. R. Hoare, 1962)
 Time bounds for selection (by Manual Blum, Robert W. Floyd, Vaughan Pratt, Ronald Rivest, and Robert E. Tarjan, 1973)
 Expected time bounds for selection (by Robert W. Floyd, Ronald L. Rivest, 1973)
 Ph. D. thesis of Michael Ian Shamos (Section 6.2: ClosestPoint Problems)
 Finding and counting given length cycles (by Noga Alon, Raphael Yuster, and Uri Zwick, 1994)
 Closet Pair Data Structure: Applications (by David Eppstein)
 Dynamic Euclidean Minimum Spanning Trees and Extrema of Binary Functions (by David Eppstein, 1995)
 Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs (by David Eppstein, 1998)
 Fourier analysis (by Cleve Moler)
 A general method for solving divideandconquer recurrences (by J. L. Bentley, D. Haken, J. B. Saxe, 1980)
 The complexity of computations (by A. A. Karatsuba, 1995) ,
 Sorting and selection on dymamic data (by Aris Anagnostopoulos, et al, 2011) ,
 Gaussian eliminination is not optimal (by V. Strassen, 1969)
 Matrix multiplication via arithmetic progressions (by Don Coppersmith, Shmuel Winograd, 1990) ,
 Gene coexpression measures in large heterogeneous samples using count statistics (by Y. X. Rachel Wang, Michael S. Watewrman, and Haiyan Huang, 2014) ,

Week 3, 4, 5: More on basic algorithm design techniques;

Lecture 4: Dynamic programming technique;
Lec6.pdf ;
Lec6HMM.pdf ;
RNA secondary structure prediction (by Sarah Aerni) ; Edit distance (by Andrew McCallum);

Reading material:
 Chapter 2,15,16,7,33.4 of Introduction to Algorithms,
 Chapter 5,4,6 of Algorithm design,
 On Efficient Computation of Matrix Chain Products (by S. S. Godbole, 1973)
 An O(n log n) algorithm for computation of matrix chain products (by T. C. Hu and M. T. Shing, 1981)
 A general method applicable to the search for similarities in the amino acid sequence of two proteins (by Saul B. Needleman, Christian D. Wunsch, 1970)
 Identification of Common Molecular Subsequences (by T.F.SMITH and M. S. WATERMAN, 1981)
 The statistical distribution of nucleic acid similarities (by T.F.SMITH, M. S. WATERMAN, and C. Burks, 1985)
 Esitmating statistical significance of sequence similarities (by M. S. WATERMAN, 1994)
 Implementation of the SmithWaterman Algorithm on a Reconfigurable Supercomputing Platform (White paper by ALTERA, 2007)
 A linear space algorithm for computing maximal common subsequences (by D. S. Hirschberg, 1975)
 Rapid similarity searches of nucleic acid and protein data bank (by W. J. Wilbur and D. J. Lipman, 1983)
 Fast optimal alignment (by James W. Ficket, 1984)
 A short note on dynamic programming in
a band optimal alignment (by JeanFrancois Gilbrat, 2018)
 Basic Local Alignment Search Tool (by S. Altschul, et al. 1990)
 Pvalue calculation (by J. Zhang, 2007)
 PAM matrix for BLAST algorithm (by C. Alexander, 2002)
 On a routing problem (by Richard Bellman, 1958)
 All pair shorest path
 Advanced dynamic programing
 Richard Bellman on the birth of dynamic programming (by Stuart Dreyfus, 2002)
 Computing Partitions with Applications to the Knapsack problem (by E. Horowitz and S. Sahni, 1974)
 The rise and fall of Knapsack cryptosystems (by A. M. Olyzko, 1994)
 A dynamic programming approach to sequencing problems (by Michael Held and Richard M. Karp, 1962)
 Knapsack problems (by Hans Kellerer, Ulrich Pferschy, and David Pisinger, 2003)
 Publickkey cryptosystem (by Charles Clancy)

Week 5, 6, 7: Still more on basic algorithm design techniques;

Lecture 5: Greedy technique
Lec7.pdf ;
demo of Dijkstra's algorithm ;
demo of Interval Scheduling algorithm (by K. Wayne),
Lec7Heap.pdf ;
Lec7UnionFind.pdf ;
DemoBinaryHeap.pdf (by Kevin Wayne) ,
DemoHeapify.pdf (by Kevin Wayne) ,

Lecture 2: Basic algorithm analysis techniques, worstcase, averagecase, and amortized analysis;
Lec2.pdf ,
demo of TableInsert (by C. Leiserson),

Reading material:
 Chapter 2,15,16,7,33.4 of Introduction to Algorithms,
 Chapter 5,4,6 of Algorithm design
 a note by Sleator ,
 A note on two problems in connexion with graphs (by E. W. Dijkstra, 1959)
 Algorithm 97: Shortest path (by Robert W. Floyd, 1962)
 Topdown analysis of path compression (by Raimund Seidel and Micha Sharir, 2005)
 Set merging algorithms (by Hopcroft J. E., Ullman J. D., 1973)
 Efficiency of equivalence algorithms (by M. Fischer, 1972)
 Efficiency of a good but not linear set union algorithm (by R. Tarjan, 1975)
 Worstcase analysis of set union algoritms (by R. Tarjan, 1984)
 A theorem on Boolean matrics (by Stephen Warshall, 1962)
 Efficient algorithms for shortest paths in sparse networks (by Donald B. Johnson, 1977)
 Disjoint paths in networks (by J. W. Suurballe, 1974)
 An interview with Edsger W. Dijkstra (Conducted by Philip L. Frana 2001)
 On the shortest spanning subtree of a graph and the traveling salesman problem (by Joseph B. Kruskal Jr., 1955)
 Shortest Connection Networks and Some Generalizations (by Robert. C. Prim, 1957)
 A Mathematical Theory of Communication (by C. E. Shannon, 1948)
 An interview with Claude Shannon (Conducted by Robert Price, 1982)
 An interview with Robert M. Fano (Conducted by Arthur L. Norberg, 1989)
 A Method for the Construction of MinimumRedundancy Codes (by DAVID A. HUFFMAN, 1952)
 Profile: David A. Huffman Encoding the “Neatness” of Ones and Zeroes (by Gary Stix, 1991)
 Binary Essence: Various aspects of data compression
 Algorithm 245, TreeSort 3 (by Robert M. Floyd, 1964)
 Discovery of Huffman Codes (by Inna Pivkina, 2010)
 Binomial Heap Script (by Sotirios Stergiopoulos, 2001)
 Fibonacci Heap Animation (by Jason Huang Hu and Wei Wang, 2003)
 What is a matroid? (by James Oxley, 2003)
 On the abstract properties of linear dependence (by Hassler Whitney, 1935)
 Nonseparable and planar graphs (by Hassler Whitney, 1932)
 Matroids and greedy algorithms(by Jack Edmonds, 1971)
 A Data Structure for Manipulating Priority Queues (by Jean Vuillemin, 1978) ,
 Fibonacci heaps and their uses in improved network optimization algorithms (by M. Fredman and R. Tarjan, 1987) ,
 Robert Tarjan  the art of the algorihtms (by Jamie Beckett, 2004) ,
 Amortized Analysis Explained (by Rebecca Fiebrink)

Week 8, 9: Linear programming

Lecture 6: Linear programming: Simplex algorithm
Lec8.pdf ,
Lec8SecretaryProblem.pdf ,
Lec8GenomeRearrangeProblem.pdf ,
an example of cycling in simplex algorithm (given by E. M. L. Beale, 1955),
an example of KleeMinty cube,
a script to generate KleeMinty cube (with noise),
a script to generate KleeMinty cube (without noise),
the DIET problem (in.math format) ,

Reading material:
 Chapter 29 of Introduction to Algorithms, Combinatorial optimization: algorithm and complexity.
 The life and times of the father of linear programming (by Saul I. Gass) ,
 An interview with George B. Dantzig: the farther of linear programming (Conducted by Watts, Griffis and McOuat, 1986) ,
 Mathematical Methods of Organizing and Planning Production (by L. Kantorovich, 1939) ,
 The First Algorithm for Linear Programming: An Analysis of Kantorovich's Method (by C. van de Panne and F. Rahnama, 1985) ,
 CONCEPTS OF OPTIMALITY AND THEIR USES (Nobel memorial lecture, by T. Koopmans, 1975) ,
 Mathematics in Economics: Achievements, Difficulties, Perspectives (Nobel memorial lecture, by L. Kantorovich, 1975) ,
 The diet problem (by George B. Dantzig, 1990) ,
 A primaldual algorithm (by George B. Dantzig, L. R. Ford, D. R. Fulkerson 1956) ,
 The cost of subsistence (by George Stigler, 1945) ,
 Linear programming (by George B. Dantzig, 2002) ,
 Linear programming and extensions PART I (by George B. Dantzig, 1963) ,
 Linear programming and extensions PART II (by George B. Dantzig, 1963) ,
 Ellipsoid Method
(by Steffen Rebennack, 2008) ,
 Lecture notes on the ellipsoid algorithm (by Michel Goemans, 2009) ,
 The Ellipsoid Method: A Survey
 PrimalDual methods for linear programming (by Philip E. GILL, Walter MURRAY, Dulce B. PONCELEON and Michael A. SAUNDERS, 1994) ,
 Interior point methods and linear programming (by Robert Robere, 2012) ,
 ON PROJECTED NEWTON BARRIER METHODS FOR
LINEAR PROGRAMMING AND AN EQUIVALENCE TO
KARMARKAR'S PROJECTIVE METHOD (by Philip E. Gill, Walter MURRAY, Michael A. SAUNDERS, J.A. TOMLIN, Margaret H. WRIGHT, 1986) ,
 A new polynomialtime algorithm for linear programming (by N. Karmarkar, 1984) ,
 C++ implementation of Khachiya algorithm for the minimum enclosing (or covering) ellipsoid (by Bojan Nikolic) ,
 In memoriam: Leonid Khachiyan ,
 KleeMinty example (by H. Greenberg) ,
 Simplex examples ,
 Smoothed complexity (by D. Spielman and S. Teng) ,
 Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time (by D. Spielman and S. Teng, 2001) ,
 GLPK (GNU Linear Programming Kit
 A new polynomialtime algorithm for linear programming (by N. Karmarkar, 1984) ,
 The interiorpoint revolution in optimization: history, recent developments, and lasting consequences (by Margaret H. Wright, 2004) ,
 Why a pure primal Newton barrier step may be infeasible? (by Margaret H. Wright, 1995) ,
 Numerical Optimization (by Nocedal, Jorge, Wright, S., 2006) ,
 Solving Inequalities and Proving Farkas’s Lemma Made Easy (by David Avis and Bohdan Kaluzny) ,
 Week 10, 11: Linear programming (cont'd)

Lecture 9: Linear programming: duality;
Lec9.pdf ,
A gnuplot script to illustrate Lagrangian dual ,
Lec9DIET.math ,
Lec9DIETDual.math ,
Lec9DIETb12001.math ,
Lec9DIETb256.math ,
Lec9DIETb3801.math

Reading material:
 Chapter 29 of Introduction to Algorithms,
 Combinatorial optimization: algorithm and complexity.
 On the theory of games of strategy (by John von Neumann, 1928) ,
 NonCooperative Games (by John Nash, 1951) ,
 Zerosum Twoperson Games (by T. E. S. Raghavan, 1994) ,
 KKT Examples (by Stanley B. Gershwin) ,
 KKT conditions and applications (by Michel Baes) ,
 Duality and KKT conditions (by S. Cui) ,
 Lagrangian Multipliers Revisited (by Morten Slater, 1950) ,
 The Lagrangian Relaxation Method for Solving Integer Programming Problems (by Marshall Fisher, 2004) ,
 Lagrange relaxation and KKT conditions () ,
 Applied integer programming  modelling and solution
 Week 12, 13: Network flow

Lecture 10: Network flow and its applications;
Lec10.pdf ,
Networkflow applications ,
demo of FordFulkerson algorithm ,
,
demo of EdmondsKarp algorithm ,
demo of Dinic algorithm ,
Irrational capacities might lead to endless iterations ,
 Reading material:
 Chapter 26 of Introduction to Algorithms,
 Chapter 7 of Algorithm design, Combinatorial optimization: algorithm and complexity,
 Networkflow research history (by A. Schrijver) ,
 Maximal flow through a network (by L. R. Ford Jr. and D. R. Fulkerson, 1956) ,
 Efficient
Maximum
Flow
Algorithms (by Andrew V. Goldberg, and Robert Tarjan, 2014) ,
 The exact time bound for a maximum flow algorithm applied to a set of representative problems (by A. Karzanov, 1973) ,
 Determining the maximal flow in a network by the method of preflows (by A. Karzanov, 1974) ,
 Determinining the maximal flow in a network by the method of preflows (by A. Karzanov, 1974) ,
 Algorithm for solution of a problem of maximum flow in a network with power estimation (by E. A. Dinic, 1970) ,
 Finding minimumcost flows by double scaling (by R. A. Ahuja, A. V. Goldberg, J. B. Orlin, and R. E. Tarjan, 1992) ,
 Dinitz' Algorithm: The Original Version and Even's Version (by Yefim Dinitz, 2006) ,
 Finding disjoint paths in networks (by D. Sidhu, R. Nair, and S. Abdallsh, 1991) ,
 Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems (by Jack Edmonds and Richard M. Karp, 1972) ,
 Network Flow Algorithms (Andrew V.Goldberg, Eva Tardos and Robert E. Tarjan, 1990) ,
 Maximum Matching and a Polyhedron With O,1Vertices1 Jack Edmonds (by Jack Edmonds, 1964) ,
 Paths, Trees and Flowers ,
 Paths, Trees and Flowers (by Jack Edmonds, 1965) ,
 Faster scaling algorithms for general graph matching problems (by H. N. Gabow, R. Tarjan, 1991) ,
 A Scaling Algorithm for Maximum Weight Matching in Bipartite Graphs (by Ran Duan, HsinHao Su, 2012) ,
 Efficient Algorithms for Finding Maximal Matching in Graphs (by Zvi Galil, 1983) ,
 LinearTime Approximation for Maximum Weight Matching(by Ran Duan, Seth Pettie, 2014) ,
 MaxProduct for Maximum Weight Matching:
Convergence, Correctness, and LP Duality (by Mohsen Bayati, Devavrat Shah, and Mayank Sharma, 2008) ,
 A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems (by Morton Klein, 1967) ,
 Max flows in O(nm) time, or better (by James Orlin, 2012) ,
 Trees: A Mathematical Tool for All Seasons, including History of algorithms to find minimum cost spanning trees (by Joe Malkevitch)
 50 Years of Integer Programming 19582008: From the Early Years to the StateoftheArt, Springer, 2010 (Edited by M. Juenger, T. M. Kiebling, D. Naddef, G. L. Nemhauser, W. R. Pulleyblank, G. Reinelt, G. Rinaldi, and L. A. Wolsey)
 Finding minimumcost circulations by successive approximation ( by Andrew V. Goldberg, Robert E. Tarjan, 1987) ,
 What energy functions can be minimized via graph cuts (by Vladimir Kolmogorov, Ramin Zabih, 2004) ,
 Polyhedral Combinatorics and Combinatorial Optimization (by Alexander Schrijver) ,
 Two theorems in graph theory (by Clauder Berge, 1957) ,
 An $n^{5/2}$ Algorithm for Maximum Matchings in Bipartite Graphs (by J. Hopcroft, and R. Karp, 1973) ,
 On representatives of subsets (by P. Hall, 1935) ,
 A Primal Method for the Assignment and Transportation Problems (by M. L. Balinski and R. E. Gomory, 1964) ,
 The Hungarian Method for the Assignment Problem (by H. W. Kuhn, 1955) ,
 Variants of The Hungarian Method for Assignment Problems (by H. W. Kuhn, 1956) ,
 On the history of combinatorial optimization (by Alexander Schrijver, 2005) ,
 Jen¨o Egerv´ary: from the origins of the Hungarian algorithm to satellite communication (by Silvano Martello, 2009) ,
 On combinatorial properties of matrices (by Jeo Egervary, 1931, Translated by H. Kuhn) ,
 Solutions of games by differential equations (by G. W. Brown, von Neumann, In: H. W. Kuhn and A. W. Tucker, Eds., Contributions to the Theory of Games I, Princeton University Press, Princeton, 1950) ,
 A certain zerosum twoperson game equivalent to the optimal assignment problem (by von Neumann, In: H. W. Kuhn and A. W. Tucker, Eds., Contributions to the Theory of Games I, Princeton University Press, Princeton, 1950) ,
 Algorithms for the assignment and transportation problems (by James Munkres, 1957) ,
 A bibliography of graph matching (by Seth Pettie) ,
 Differential gene expression analysis using coexpression and RNASeq data (by Tao Jiang et al. 2013) ,
 Week 14, 15: Problem intrinsic property: Hardness

Lecture 11: Problem hardness: Polynomialtime reduction;
Lec3.pdf

Reading material:
 Computer and intractability,
 Chapter 8 of Algorithm design,
 Chapter 34 of Introduction to Algorithms
 Reducibility among combinatorial problems (by R. M. Karp, 1972) , slides
 Molecular Computation of Solutions to Combinatorial Problems (by Leonard M. Adleman, 1994),
 Computing with DNA (by Leonard M. Adleman, 1998),
 Computer in a testtube (by Hendrik Jan Hoogeboom, 2010),
 How to apply de Bruijn graphs to genome assemly (by Phillip E. C. Compeau, Pavel A. Pevzner, and Glenn Tesler, 2011),
 Week 14, 15: NPCompleteness

Lecture 12: NPHard problems: packing problem, covering problems,
sequencing problem, partitioning, coloring, SAT, numbering problems, etc.
Lec4.pdf , Turing machine demo (by Zhen Ji) , Turing machine demo (by Andrew Hodges, Turing machine (by K. Wayne) , Computability (by K. Wayne) , 2SAT is in P (by D. Moshko ) ,

Reading material:
 Week 16, 17: Solving hard problems: approximation and randomization
 Week 18: Solving hard problems: approximation and randomization

Week 19: Solving hard problems: special cases and heuristics
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