In the popular computer game of Tetris, the player is given a sequence of tetromino pieces and must pack them into a rectangular gameboard initially occupied by a given configuration of filled squares; any completely filled row of the gameboard is cleared and all pieces above it drop by one row. We prove that in the offline version of Tetris, it is NP-complete to maximize the number of cleared ...

We give an exposition of Cai, Pavan and Sivakumar’s result on the hardness of permanent. They show that assuming it is hard to compute the permanent in the worst case, an algorithm cannot compute the permanent correctly even on (say) a 1/n fraction of the inputs.

though the fields of regenerative dentistry and tissue engineering have undergone significant advancements, yet its application to the field of implant-dentistry is lacking; in the sense that presently the implants are being placed with the aim of attaining osseointegration without giving consideration to the regeneration of periodontium around the implant. the following article reveals the cli...

Clickomania is a classic computer puzzle game (also known as SameGame, Chain-Shot!, and Swell-Foop, among other names). Originally developed by Kuniaki “Morisuke” Moribe under the name Chain-Shot! for the Fujitsu FM-8, and announced in the November 1985 issue of ASCII Monthly magazine, it has since been made available for a variety of digital platforms [Mor03]. Figure 1 shows some examples. Alt...

Let G = (V, E) be a graph. Let k ≤ |V | be an integer. Let O k be the number of edge induced subgraphs of G having k vertices and an odd number of edges. Let E k be the number of edge induced subgraphs of G having k vertices and an even number of edges. Let ∆ k = O k − E k. The Odd Even Delta problem consists in computing ∆ k , given G and k. We show that such problem is #P-hard, even on 3-regu...

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfactory approximation ratios, and those that guarantee high quality ratios but are slow. In this article we prove that this tradeoff between running time and solution quality is unavoidable. For the problem a minimum number of edges in a graph need to be found that, when c...