PPT-On Problems as Hard as CNF-Sat

Joint work with Marek Cygan Holger Dell Daniel Lokshtanov Daniel Marx Yoshio Okamoto Ramamohan Paturi Saket Saurabh and Magnus Wahlstrom CCC 2012 Jesper Nederlof Utrecht University The Netherlands. 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.”. vs. Algebraic. Computational Problems. Boaz Barak – MSR New England. Based on joint works with Benny Applebaum, Guy Kindler, . David . Steurer, . and . Avi Wigderson . Erd. ő. s Centennial, Budapest, July 2013. T. heory. Intractable problems. Online Cryptography Course Dan Boneh. Easy problems. Given composite N and x in Z. N . . find x. -1. . in Z. N . Given prime p . 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). 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. Learning Outcome Assessment 1. ASSE 2111 – Section. Mashail. AlHussan 200800211. Basma. . Alqahtani. . Reem. . AlGarawi. 200900379. Outline. Introduction.. How Skilled is Your Thinking (Right Now)?. 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. Rob Sherwood. SDNRG – Atlanta, November 2012. Outline. Level Setting and Framework. Sexy. problems. (that I’m not going to talk about). My. (not so sexy) . Problems. Forwarding Memory Abstractions. 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 . Given an algorithm A that solves a problem.. If the worst case time efficiency of A is O(p(n)), for some polynomial p, then A is said to solve the problem in . polynomial time. .. If a problem can be solved in polynomial time it is said to be . 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).