Lecture 3 : 1 vs 3 / 4 + 2 Hardness for Max - Coverage Jan 22 , 2008

نویسنده

  • Ravishankar Krishnaswamy
چکیده

The MAX-LABEL-COVER(K,L) Problem: An instance to the MAX-LABEL-COVER(K,L) problem comprises of a bipartite graph G(U, V, E) with U and V being the two partitions, and a projection function πv→u : L → K on each edge (u, v). The objective is to obtain a labeling of the vertices (a function f : U → K, V → L) which satisfies maximum fraction of the edges. Edge (u, v) is satisfied by labeling f if and only if f(u) = πv→u(f(v)). Figure 1 describes such an instance. The following theorem has been proved by Raz.

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

Advanced Approximation Algorithms ( CMU 15 - 854 B , Spring 2008 ) Lecture 22 : Hardness of Max - E 3 Lin April 3 , 2008

This lecture is beginning the proof of 1 − ǫ vs. 1/2 + ǫ hardness of Max-E3Lin. The basic idea is similar to previous reductions; reduce from Label-Cover using a gadget that creates 2 variables corresponding to the key vertices and 2 vertices corresponding to the label vertices, where they correspond in the usual way to {0, 1} and {0, 1}. We then want to select some subsets x, y, z of these str...

متن کامل

Lecture 24 : Hardness of approximation of MAX - CUT April 10 , 2008

• The 1 vs 1 decision problem is easy for MAX-CUTas the problem is equivalent to testing if the graph is bipartite. • Goemans-Williamson's SDP based algorithm for MAX-CUTyields a 1 2 (1−ρ) vs (arccos(ρ))/π approximation for all ρ < −0.69. Replacing ρ with 2δ − 1 shows that the 1 − δ vs 1 − Θ(√ δ) problem is easy. If we think about MAX-CUTas MIN-UNCUT, this would mean that the δ vs Θ(√ δ) proble...

متن کامل

Recap: Consistent-labeling and Hypercubes

Universes. In many cases, it is probably more convenient or even crucial to work with an abstract universe, rather than a collection of Boolean hypercubes. Suppose we are given an abstract universe A = ⊎ eAe, where the subuniverses all have the same size. Like before, we want the property that unless both sets in a complement pair are picked, picking a large number of sets still won’t cover the...

متن کامل

Advanced Approximation Algorithms ( CMU 15 - 854 B , Spring 2008 ) Lecture 25 : Hardness of Max - k CSPs and Max - Independent - Set

Recall that an instance of the Max-kCSP problem is a collection of constraints, each of which is defined over k variables. A random assignment to the variables in a constraint satisfies it with probability 1/2, so a random assignment satisfies a 1/2 fraction of the constraints in a Max-kCSP instance in expectation. This shows that the hardness result is close to optimal, since there is a trivia...

متن کامل

Inapproximability of Minimum Vertex Cover

Last time we examined a generic approach for inapproximability results based on the Unique Games Conjecture. Before, we had already shown that approximating MAX-3-LIN to within a constant factor larger than 12 is NP-hard. To do this we used a tweaked version of our dictatorship test that we came up with earlier in the semester. Last time we (re)proved that approximating MAX-3-LIN to within a co...

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 2008