Parameterized Study of the Test Cover Problem

We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together with a collection, $\cal T$, of distinct subsets of these items called tests. We assume that $\cal T$ is a test cover, i.e., for each pair of items there is a test in $\cal T$ containing exactly one of these items. The objective is to find a minimum size subcollection of $\cal T$, which is still a test cover. The generic parameterized version of {\sc Test Cover} is denoted by $p(k,n,|{\cal T}|)$-{\sc Test Cover}. Here, we are given $([n],\cal{T})$ and a positive integer parameter $k$ as input and the objective is to decide whether there is a test cover of size at most $p(k,n,|{\cal T}|)$. We study four parameterizations for {\sc Test Cover} and obtain the following: (a) $k$-{\sc Test Cover}, and $(n-k)$-{\sc Test Cover} are fixed-parameter tractable (FPT). (b) $(|{\cal T}|-k)$-{\sc Test Cover} and $(\log n+k)$-{\sc Test Cover} are W[1]-hard. Thus, it is unlikely that these problems are FPT

On the Seasonal and Day to Day Variations in the F2 Region

Thermoelectric scatter measurements on seasonal and daily variations in F region electron concentratio

Multidimensional Binary Vector Assignment problem: standard, structural and above guarantee parameterizations

In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called \BVA). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary vectors of size $p$. An output is a set of $n$ disjoint $m$-tuples of vectors, where each $m$-tuple is obtained by picking one vector from each set $V^i$. To each $m$-tuple we associate a $p$ dimensional vector by applying the bit-wise AND operation on the $m$ vectors of the tuple. The objective is to minimize the total number of zeros in these $n$ vectors. mBVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing. We provide for this problem FPT algorithms and negative results ($ETH$-based results, $W$[2]-hardness and a kernel lower bound) according to several parameters: the standard parameter $k$ i.e. the total number of zeros), as well as two parameters above some guaranteed values.Comment: 16 pages, 6 figure

Image Segmentation Using Dynamic Region Merging

In region merging the there are two essential issues first is order of merging and second one is stopping criterion. This work addresses two issues which are solved by Dynamic region merging algorithm which is defined by SPRT and the minimal cost criterion. The process is start from an oversegmented image, then neighboring regions are progressively merged if there is an evidence for merging. The final result is based on the observed image. This algorithm also satisfies the certain global properties of segmentation. In this algorithm region merging process become faster due to nearest neighbor graph in each iteration. The performance of dynamic region merging algorithm is shown on natural images

Weak and strong regimes of incompressible magnetohydrodynamic turbulence

It is shown that in the framework of the weak turbulence theory, the autocorrelation and cascade timescales are always of the same order of magnitude. This means that, contrary to the general belief, any model of turbulence which implies a large number of collisions among wave packets for an efficient energy cascade (such as the Iroshnikov-Kraichnan model) are not compatible with the weak turbulence theory.Comment: Accepted to Phys. Plasma