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We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n 3) and O(n 10), in the convex and general case, respectively. We then apply similar methods to prove an n O(log(n))(More)
We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O. Apart from that, we consider partitions of the plane into two sets whose common boundary is a union of piecewise linear curves. We show that for any such partition(More)
Consider a hypergraph H d n where the vertices are points of the d-dimensional combinatorial cube n d and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of H d n , i.e., permutations of points of n d preserving the edges. In this paper we provide a complete characterization. Moreover,(More)
Given the high costs of conducting a drug-response trial, researchers are now aiming to use retrospective analyses to conduct genome-wide association studies (GWAS) to identify underlying genetic contributions to drug-response variation. To prevent confounding results from a GWAS to investigate drug response, it is necessary to account for concomitant(More)
The pattern matching problem with swaps is to find all occurrences of a pattern in a text while allowing the pattern to swap adjacent symbols. The goal is to design fast matching algorithm that takes advantage of the bit parallelism of bitwise machine instructions. We point out a fatal flaw in the algorithm proposed by Ahmed et al. [The swap matching(More)
Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indexes, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial orders and consider the problem of identifying an initially unknown vertex in a tree by asking edge queries: an edge query e(More)