295 research outputs found
Composable Art: Objects that can be arranged in many ways
Abstract The concept of composable art is introduced and four examples of composable art objects are given. We analyze the number of different compositions that can be made for each object using combinatorics and the dynamic programming technique
Topological Stability of Kinetic -Centers
We study the -center problem in a kinetic setting: given a set of
continuously moving points in the plane, determine a set of (moving)
disks that cover at every time step, such that the disks are as small as
possible at any point in time. Whereas the optimal solution over time may
exhibit discontinuous changes, many practical applications require the solution
to be stable: the disks must move smoothly over time. Existing results on this
problem require the disks to move with a bounded speed, but this model is very
hard to work with. Hence, the results are limited and offer little theoretical
insight. Instead, we study the topological stability of -centers.
Topological stability was recently introduced and simply requires the solution
to change continuously, but may do so arbitrarily fast. We prove upper and
lower bounds on the ratio between the radii of an optimal but unstable solution
and the radii of a topologically stable solution---the topological stability
ratio---considering various metrics and various optimization criteria. For we provide tight bounds, and for small we can obtain nontrivial
lower and upper bounds. Finally, we provide an algorithm to compute the
topological stability ratio in polynomial time for constant
Π Π°Π·Π²ΠΈΡΠΈΠ΅ ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΠΎ-ΠΊΡΠ΅Π΄ΠΈΡΠ½ΠΎΠΉ ΠΈΠ½ΡΡΠ°ΡΡΡΡΠΊΡΡΡΡ Π½Π°ΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΈ
We introduce a variation of unit-distance graphs which we call emph clear unit-distance graphs. They require the pairwise distances of the representing points to be either exactly 1 or not close to 1. We discuss properties and applications of clear unit-distance graphs
Distributed ranking methods for geographic information retrieval
Geographic Information Retrieval is concerned with retrieving documents that are related to some location. This paper addresses the ranking of documents by both textual relevance and spatial relevance. To this end, we introduce distributed ranking, where similar documents are ranked spreaded in the list instead of sequentially. The effect of this is that documents close together in the ranked list have less redundant information. We present various ranking methods and efficient algorithms for them
Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams
This paper introduces two new abstract morphs for two 2-dimensional shapes. The intermediate shapes gradually reduce the Hausdorff distance to the goal shape and increase the Hausdorff distance to the initial shape. The morphs are conceptually simple and apply to shapes with multiple components and/or holes. We prove some basic properties relating to continuity, containment, and area. Then we give an experimental analysis that includes the two new morphs and a recently introduced abstract morph that is also based on the Hausdorff distance [Van Kreveld et al., 2022]. We show results on the area and perimeter development throughout the morph, and also the number of components and holes. A visual comparison shows that one of the new morphs appears most attractive
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