Limits of Approximation Algorithms 18 Mar , 2010 ( TIFR ) Lec . 7 : Low degree testing ( Part I )

Limits of Approximation Algorithms 25 Feb , 2010 ( TIFR ) Lec . 5 : 2 - query PCPs and BLR - Linearity Testing

Completeness ∀x ∈ L, ∃π, Pr[V π(x) accepts ] ≥ c. Soundness ie. ∀x / ∈ L, ∀π, Pr[vπ(x) accepts ] ≤ s. When Σ = {0, 1}, we will not mention it. Remark 5.1.3. • If the proof is over a binary alphabet and we have perfect completeness (i.e., c = 1) then Q ≥ 3 unless P 6= NP. Suppose we had a 2-query PCP over binary alphabet for a language L with c = 1, then L ≤p 2SAT: for each input x and random co...

Lec . 8 : Low degree testing ( Part II )

Lec . 2 : Approximation Algorithms for NP - hard Problems ( Part II )

We will continue the survey of approximation algorithms in this lecture. First, we will discuss a (1+ε)-approximation algorithm for Knapsack in time poly(n, 1/ε). We will then see applications of some heavy hammers such as linear programming (LP) and semi-definite programming (SDP) towards approximation algorithms. More specifically, we will see LPbased approximation for MAXSAT and MAXCUT. In t...

Lec . 1 : Approximation Algorithms for NP - hard problems

In this course, we will be studying, as the title suggests, the approximability and inapproximability (limits of approximability) of different combinatorial optimization problems. All the problems we will be looking at will be ones that lack efficient algorithms and in particular will be NP-hard problems. The last two-three decades has seen remarkable progress in approximation algorithms for se...

Brightness Suppression of Relativistic Radio Jets of Quasars: the Role of the Lower Electron Energy Cut-off

Although the possibility of a low energy cut-off (LEC) of the relativistic electron population (Emin ∼ 0.1 GeV) in the different components of radio galaxies has been discussed in the literature, from both theoretical and observational viewpoints, its possible role in causing a distinct spectral flattening, and thus reducing the apparent brightness temperature of the radio nucleus, has thus far...