Algorithmic Lower Bounds : Fun With Hardness Proofs Fall 2014 Lecture 3 Scribe Notes

نویسنده

  • Erik Demaine
چکیده

Last time, we established the hardness of two fundamental problems, (2-)Partition and 3-Partition, and exhibited a bunch of reductions from those problems to other numerical and geometrical ones. Today, we continue with reductions from 3and 2-Partition to geometrical problems—we’ll also use the fact that the problem of packing n squares into a square without rotations is strongly NP-complete, as we showed last time.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lower Bounds : Fun With Hardness Proofs Fall 2014 Lecture 11 Scribe Notes

Recall that one of the most commonly used reductions is the L-reduction, introduced by Papadim­ itriou and Yannakakis in [?]. This reduction consists of a pair of polynomial mappings (f(.), g(.)) where f maps an instance x of the problem A we are reducing from to an instance x/ of the problem B we are reducing to, and g maps a feasible solution y/ (of x/ i.e. instance of B) to a feasible soluti...

متن کامل

CMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Quadratic Hardness and the 3-SUM Problem

In the previous lecture, we looked at the APSP problem and some of the other closely related problems. We studied the cubic hardness of these problems. In this lecture, we will go about doing something similar, but in the domain of quadratic hardness. With regard to this, we will choose 3-SUM problem as the representative problem. We will look at some related problems, that can be reduced to th...

متن کامل

CMSC 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 کامل

CMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Introduction to Streaming Algorithms

In the previous lectures, we looked at the online algorithms and studies some of the related problems. Now we look into streaming algorithms, which have many similarities with online algorithm. They both require decisions before seeing all data but streaming algorithms can defer actions with limited memory. In these two lectures, we introduce streaming algorithms, related communication complexi...

متن کامل

CMSC 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015