CMSC 858 F : Algorithmic Lower Bounds Fall 2014 3 - SAT and NP - Hardness
نویسندگان
چکیده
The most important NP-Complete (logic) problem family!
منابع مشابه
CMSC 858 F : Algorithmic Lower Bounds Fall 2014 Puzzles and Reductions from 3 - Partition
In this lecture, we first examine several classes of NP-hardness and polynomial time algorithms which arise from differences in how integers are encoded in problem input. We then look at the 3-partition problem, which is very useful for proving the strongest notion of NP-hardness. Finally, we use reduction from 3-partition to prove NP-hardness for a handful of problems, including a set of 4 pac...
متن کاملCMSC 858F: Algorithmic Lower Bounds Fall 2014 Parameterized reductions and assumptions
Definition 1 ETH: there is no 2 time algorithm for n variable 3-SAT. (the current best bound is 1.30704 [1]). Note that an n-variable 3-SAT can have Ω(n) clauses but Impagliazzo et al. [2] show that there is a 2-time algorithm for n-variable 3-SAT iff there is a 2-time algorithm for m-clause 3-SAT. Thus ETH also says: There is no 2-time algorithm for m-clause 3-SAT. The standard textbook NP-har...
متن کاملCMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Fixed Parameter Algorithms and Lower Bounds for parameterized Problems
Unless P = NP we have to satisfy ourselves with any two out of the three goals. Most of the early undergrad algorithms like matching, shortest path etc. are exact and fast. To tackle hard problems and obtain a fast solution we use approximation algorithms, PTAS etc. FPT or fixed parameter tractable algorithms come to our rescue when we need to tackle hard problems yet obtain an optimal solution...
متن کاملCMSC 858F: Algorithmic Lower Bounds Fall 2014 Approximation Hardness
Assuming P 6=NP we cannot satisfy all three goals together. Therefore we need to sacrifice at least one of the goals. If we give up on solving hard problems we can only wish for solving a very small fraction of algorithmic problems and the solutions are usually well-known methods that we learned in undergraduate courses. If we don’t want to sacrifice the correctness and we still want to solve h...
متن کاملCMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Cubic hardness and all-pair shortest paths
In the next two lectures, we look at lower bounds conjectured on two important and well-known problems. One is the All-Pairs-Shortest-Path(APSP) problem which is believed to be truly cubic(i.e. there is no exact algorithm for this problem which runs in time O(n ) for a constant > 0). The second problem considered is the 3−SUM problem which is conjectured to be truly quadratic(i.e. there is no e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014