1. 1/15 Advanced Graph Algorithms (I) What we do not cover but you are expected to know –Mathematical induction, basic data structure, sorting, shortest path, minimum spanning tree, dynamic programming, divide-and-conquer –Homework assignment Better if you know NP-completeness, NP- hard –Pick it up yourself if not. It becomes a common sense in computer science.

2. 2/15 Advanced Graph Algorithms (II) Who should take – 對演算法有興趣，喜歡接受挑戰 – 對抽象思考有興趣 – 培養基礎，以後有志於從事研究工作 – 有興趣將理論應用到實際問題 生物資訊，網路搜尋，自然語言 Who should not – 說不出有什麼特別的興趣，也沒有特別想學到些 什麼，只是當成一般選修課 – 不想花時間

3. 3/15 Scope planar graphs consecutive ones property interval graphs maximal planar graphs physical mapping algorithms clone assembly NMR backbone assignment Pattern recognition (motif) shot-gun sequencing 論文 presentation (many more applications) program (LEDA programming)

4. 4/15 Grading (I) Be punctual （準時出席） In-class Question answering –Ask a question pointing out some important things I might have missed or about some possible variations of materials covered –Answer a question I raised in class –Leave chances to others if you have asked one already during the day unless no one else could answer – 這部分佔總成績 10 分

5. 5/15 Grading (II) Programming project –Implementing one of the algorithms taught in class or a special related algorithm Paper presentation –Announce by 10/9, make selection by 10/23 –Rehearse with the teaching assistants –Can pick your own paper and get approval from me

6. 6/15 Biography (I) 許聞廉 Wen-Lian Hsu 1973 台大數學學士 1980 康乃爾 Operations Research 博士 1980-89 美國西北大學工業工程系 1989- 中央研究院資訊所 Research interests: –Design of algorithms, artificial intelligence, natural language processing, bioinformatics, knowledge management

7. 7/15 A Hat Problem (5) No strategy In the worst case, all men were shot. Strategy 1 (with collaboration) In the worst case, half of the men will be shot. N prisoners lined up in a row, each one can see the hats of all people in front of him. A person who guesses the color of his hat correctly can survive

8. 8/15 A Hat Problem (5) Design a strategy so that as few men will die as possible. Strategy 1 (at least half can survive, probably ¾ will) Divide the men into two groups: odd-numbered and even-numbered. Each odd-numbered person should tell the person in front the correct color (since he can see it). As for the person himself, there is still ½ chance that he will survive)

9. 9/15 A Hat Problem (5) Message Passing Suppose we use 0 to indicate white hat and 1 for black hat Let the original sequence be Then the sequences each man will see are as follows 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 How do you let each man guess the right # (except the first one)? odd-evenness (or parity) of the # of 0’s and 1’s.

10. 10/15 A Hat Problem (5) If the current hat is 0, then moving to the next sequence will only change the parity of 0 (the parity of 1 stays the same) Everyone knows the parity of 0 and 1 for the sequence in front of him. If the 1 st person says the parity of 1 for his sequence (either odd or even), then by checking whether the parity of 1 changes, the 2 nd person knows his hat color By induction, everyone afterward can compute his hat color 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1

11. 11/15 Marriage Theorem (7) The following condition is both necessary and sufficient: Every set of r girls, 1  r  n, like at least r boys. There are n girls and n boys. Each girl has a list of boys she can marry. Assume a boy never rejects a girl’s offer. Under what condition can you find a perfect match? Prove by induction (for the sufficient part, since necessity is clear). How do you reduce the problem size to a smaller one? Easy case: There is a subset of k girls who like exactly k boys By induction, can match these k girls with the k boys. Similarly, the remaining n-k girls can be matched to the n-k boys Hard case: Every set of r girls, 1  r  n, likes > r boys. Marry a girl with a boy first, then for the remaining n-1 girls and n-1 boys, the condition still holds.

12. 12/15 Common Computational Models Discrete algorithm –Probabilistic, approximation, on-line, randomized Non-linear programming (numerical) Statistical –Regression –Machine learning Neural net, SVM, Hidden Markov Model, Maximum entropy, Conditional random fields, –Evolutionary Genetic algorithm, particle swarm Areas: NLP, ASR, IR, IE, DM

13. 13/15 Homework Assignment This is for a review of your previous algorithm courses You have two weeks to work on it –Should not take too much time Probably the only assignment for the semester 助教：楊翊文

14. 14/15 Notations Graph G = (V, E). (some called network) –Vertex, node |V| = n –edge (directed, undirected), link |E| = m Loop, multiple edges –Adjacent, incident, neighbor Simple graph –No loop, no multiple edges Subgraphs, induced subgraphs K-connected graph –Connected, biconnected, …