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We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type results typically bound the maximum number...

A common subproblem of $DNF$ approximate counting and derandomizing $RL$ is the discrepancy problem for combinatorial rectangles. We explicitly construct a $poly(n)$size sample space that approximates the volume of any combinatorial rectangle in $[n]^n$ to within $o(1)$ error (improving on the constructions of [EGLNV92]). The construction extends the techniques of [LLSZ95] for the analogous hit...

Path testing a program involves generating all paths through the program, and finding a set of program inputs that will execute every path. Since it is impossible to cover all paths in a program, path testing can be relaxed by selecting a subset of all executable paths that fulfill a certain path selection criterion and finding test data to cover it. The automatic generation of such test paths ...

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon...

EDITOR’S NOTE Geopersia is published biannually by the College of Science, University of Tehran, Iran. The College of Science published “Journal of Science”, which covered all fields of basic science, from 1968 to 2010. It was then decided that the College’s journals should be more specialized, and hence publication of Geopersia was launched. Geopersia aims to publish peer-reviewed original...

the vital need for river management is understood and predict of bank erosion processes. almost models will not be able to evaluate bank erosion,accurately. bstem model is the most usable model in many of river engineering projects in the world. necessary data for this model are related to driving and resisting forces controlled by hydraulic and geotechnical processes. these data include geomet...