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Pebble motion problems occur in domains such as multi-robot motion planning (in which the pebbles are robots) and network routing (in which the pebbles are packets of data). The best-known example of a pebble motion problem is the famous 15 puzzle where a disordered group of fifteen tiles must be rearranged within a 4x4 grid by sliding one tile ...
Opalescence or play of color is an optical phenomenon associated with the mineraloid gemstone opal, [1] a hydrated silicon dioxide. [2] This effect appears as a milky, translucent glow that changes with the angle of light, often creating a soft, pearly sheen that can display various colors or hues.
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
The final two chapters of the first edition concern generalizations of polyominoes to polycubes and other polyforms, [3] [4] and briefly mention the work of Edward F. Moore and Hao Wang proving the undecidability of certain tiling problems including the problem of whether a set of polyominoes can tile the plane. [3]
A precursor to the SMPTE test pattern was conceived by Norbert D. Larky (1927–2018) [5] [6] and David D. Holmes (1926–2006) [7] [8] of RCA Laboratories and first published in RCA Licensee Bulletin LB-819 on February 7, 1951. U.S. patent 2,742,525 Color Test Pattern Generator (now expired) was awarded on April 17, 1956, to Larky and Holmes. [9]
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).
The sheen [4] or gloss level of a paint is principally determined by the ratio of resinous, adhesive binder, which solidifies after drying, and solid, powdery pigment.The more binder the coating contains, the more regular reflection will be made from its smooth surface; conversely, with less binder, grains of pigment become exposed to the surface, scattering the light and providing matte ...
The problem of finding equitable colorings with as few colors as possible (below the Hajnal-Szemerédi bound) has also been studied. A straightforward reduction from graph coloring to equitable coloring may be proven by adding sufficiently many isolated vertices to a graph, showing that it is NP-complete to test whether a graph has an equitable ...