David Ian Olive. 16 April 1937—7 November 2012

UTMS 2012 – 16 November 14 , 2012

We establish an isoperimetric inequality with constraint by ndimensional lattices. We prove that, among all domains which consist of rectangular parallelepipeds with the common side-lengths, a cube is the best shape to minimize the ratio involving its perimeter and volume as long as the cube is realizable by the lattice. For its proof a solvability of finite difference PoissonNeumann problems i...

L 16 — April 19 , 2012

In this lecture, we consider the string matching problem finding some or all places in a text where the query string occurs as a substring. From the perspective of a one-shot approach, we can solve string matching in O(|T |) time, where |T | is the size of our text. This purely algorithmic approach has been studied extensively in the papers by Knuth-Morris-Pratt [6], Boyer-Moore [1], and Rabin-...

Lecture L 16 — April 19 , 2012

1 Overview In this lecture, we consider the string matching problem-finding some or all places in a text where the query string occurs as a substring. From the perspective of a one-shot approach, we can solve string matching in O(|T |) time, where |T | is the size of our text. This purely algorithmic approach has been studied extensively in the papers by Knuth-Morris-Pratt [6], Boyer-Moore [1],...

Lecture 16 — November 6 th , 2012 ( Prasad Raghavendra )

In this lecture, we will begin to talk about the “PCP Theorem” (Probabilistically Checkable Proofs Theorem). Since the discovery of NP-completeness in 1972, researchers had mulled over the issue of whether we can efficiently compute approximate solutions to NP-hard optimization problems. They failed to design such approximate algorithms for most problems. They then tried to show that computing ...

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