The Column Explained . . . Plus Conference Roundup, Part 2!

Column: The Physics of Digital Information-Part 2

Sums of Squares Methods Explained: Part I

Let p(~x) ∈ R[~x] be SOS in t real polynomial squares. Then, p(~x) must have even degree. Let deg(p(~x)) = 2k. Then, ∃q1, . . . , qt ∈ R[~x] s.t. deg(qi(~x)) ≤ k and p(~x) = ∑t i=1 q 2 i (~x). A key observation is that we can now exactly characterise the finitely many possible power-products that could occur in each qi(~x). Definition 1.1. Let Λn(d) = {α = 〈α1, . . . , αn〉 ∈ Nn | α1 + . . .+ αn...

The Book Review Column 1 2.1 Part 1. Dictionaries and Priority Queues 2.2 Part 2. near Neighbor Searching

In this column we review the following books. This book reports on a the DIMACS implementation where competitors really coded up different algorithms for the problems indicated. Books I want Reviewed If you want a FREE copy of one of these books in exchange for a review, then email me at gasarchcs.umd.edu Reviews need to be in LaTeX, LaTeX2e, or Plaintext. 1 Overview This book is in the area of...

Nurminen's Column on IRIS: Part 1

The First Years of IRIS IRIS is the name of the annual meeting of people involved with Information Systems Research in Scandinavia. It has been circulating among the four Scandinavian countries Denmark, Finland, Norway and Sweden now already 20 years. In August 1997 the IRIS Association was established. At the same meeting I was invited to give an opening address about the 20 years of IRIS hist...

Guest Column: Completeness in the Polynomial-Time Hierarchy: Part II

In this survey, we highlight selected complete problems from Part I of this column, and include reductions for some of them. We also discuss methods for proving hardness of approximation in the second and higher levels of the Polynomial-Time Hierarchy, and illustrate with two full proofs of non-approximability utilizing error-correcting codes.