PPT-Approximating NP-hard Problems

Efficient Algorithms and their Limits Prasad Raghavendra University of Washington Seattle Max 3 SAT Find an assignment that satisfies the maximum number of clauses Max 3 SAT Max 2. We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring Set Covering and other related minimization problems Specifi cally there is an E 0 such that Graph Coloring cannot be approximated w Richard M. Karp. Bangalore, January 5, 2011. NP-Hard Problems. The P vs. NP problem: Is finding a solution to a combinatorial search problem as easy as checking a solution. The answer is expected to be “No.”. Approximating the . Depth. via Sampling and Emptiness. Approximating the . Depth. via Sampling and Emptiness. Approximating the . Depth. via Sampling and Emptiness. Example: Range tree. S = Set of points in the plane. Equilibria. : How…. …and What’s the Point?. Yevgeniy Vorobeychik. Sandia National Laboratories. Who am I?. Ph.D. CS, University of Michigan, advised by Michael Wellman. approximating/estimating . Chairman & CEO of Complete Holdings Group. Founder of Passport Health Communications. 35 years of healthcare experience. On board of PharmMD, Patient Focus, NextGXDX, Brightstone, WMC foundation. Nattee Niparnan. Easy & Hard Problem. What is “difficulty” of problem?. Difficult. . for . computer scientist. to derive algorithm for the problem?. Difficult for . computer. to solve (run the derived algorithm) the problem?. Polynomial Problems (P Family). The set of problems that can be . solved. . in polynomial time . These problems form the P family . All problems we covered so far are in P. P. Nondeterministic Polynomial (NP Family). Shirly. . Yakubov. Motivation. Given a set . S. of n objects we . want to store them in . a . data-structure . that . could answer . range queries. For a range . r. we have. :. range-searching counting. into Computational Complexity. Bart Selman . Cornell University. Joint with Scott Kirkpatrick (IBM Research). Computational Challenges. Many core computational tasks have been shown to be . computationally intractable. Context. Final Year. 120 credits (1 credit . approx. 10 hours). 30 credit project. 4 modules in semester 1 . 4 modules in semester 2. A module is 10 credits. 1 c. ompulsory . module on Prof Issues. Students select 4 modules from 8 in each semester. Instructor. Neelima. Gupta. ngupta@. cs.du.ac.in. Presentation Edited by . Sapna. Grover. Table of Contents. NP – Hardness. Reductions. NP - . Hard. The aim to study this class is not to solve a problem but to see how hard . Shirly. . Yakubov. Motivation. Given a set . S. of n objects we . want to store them in . a . data-structure . that . could answer . range queries. For a range . r. we have. :. range-searching counting. Richard M. Karp. Bangalore, January 5, 2011. NP-Hard Problems. The P vs. NP problem: Is finding a solution to a combinatorial search problem as easy as checking a solution. The answer is expected to be “No.”. CHINMAYA KRISHNA SURYADEVARA. P and NP. P – The set of all problems solvable in polynomial time by a deterministic Turing Machine (DTM).. Example: Sorting and searching.. P and NP. NP- the set of all problems solvable in polynomial time by non deterministic Turing Machine (NDTM).