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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)

The guarding game is a game in which a set of cops has to guard a region in a digraph against a robber. The robber and the cops are placed on vertices of the graph; they take turns in moving to adjacent vertices (or staying). The goal of the robber is to enter the guarded region at a vertex with no cop on it. The problem is to find the minimum number of… (More)

We design a new class of vertex and set cover games, where the price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs. This is in contrast to all previously studied covering games, where the price of anarchy grows linearly with the size of the… (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)

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)

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)

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)

The guarding game is a game in which several cops try to guard a region in a (directed or undirected) graph against a robber. The robber and the cops are placed on the vertices of the graph; they take turns in moving to adjacent vertices (or staying), cops inside the guarded region, the robber on the remaining vertices (the robber-region). The goal of the… (More)

Tzaar is an abstract strategy two-player game, which has recently gained popularity in the gaming community and has won several awards. There are some properties, most notably the high branching factor , that make Tzaar hard for computers. We developed Waltz, a strong Tzaar-playing program, using enhanced variants of Alpha-beta and Proof-number Search based… (More)