We present several variants of the sunflower conjecture of Erdős & Rado (J Lond Math Soc 35:85–90, 1960) and discuss the relations among them. We then show that two of these conjectures (if true) imply negative answers to the questions of Coppersmith & Winograd (J Symb Comput 9:251–280, 1990) and Cohn et al. (2005) regarding possible approaches for… (More)
We present a Garey/Johnson-style list of problems known to be complete for the second and higher levels of the polynomial-time Hierarchy (polynomial hierarchy, or PH for short). We also include the best-known hardness of approximation results. The list will be updated as necessary.
We show that a number of natural optimization problems in the second level of the Polynomial Hierarchy are p 2-hard to approximate to within n factors, for specific > 0. The main technical tool is the use of explicit dis-persers to achieve strong, direct inapproximability results. The problems we consider include Succinct Set Cover, Minimum Equivalent DNF,… (More)
In this article, we present a novel technique for visualization of three-dimensional (3D) surface models, as well as its implementation in a system called AnatomyBrowser. Using our approach, visualization of 3D surface models is performed in two separate steps: a pre-rendering step, in which the models are rendered and saved in a special format, and an… (More)
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.
participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The rst section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided,… (More)
The role of symmetry (or the lack thereof) in algorithms and computational complexity.
These outstanding papers were selected in consultation with the program committee from among the twenty-nine papers that appeared in the conference. They were invited for submission and subsequently subjected to the standard refereeing process of the journal. In the paper Random arithmetic formulas can be reconstructed efficiently, by Ankit Gupta, Neeraj… (More)