Area (graph drawing)

In graph drawing, the area used by a drawing is a commonly used way of measuring its quality.

Definition

For a drawing style in which the vertices are placed on the integer lattice, the area of the drawing may be defined as the area of the smallest axis-aligned bounding box of the drawing: that is, it the product of the largest difference in x-coordinates of two vertices with the largest difference in y-coordinates. For other drawing styles, in which vertices are placed more freely, the drawing may be scaled so that the closest pair of vertices have distance one from each other, after which the area can again be defined as the area of a smallest bounding box of a drawing. Alternatively, the area can be defined as the area of the convex hull of the drawing, again after appropriate scaling.

Polynomial bounds

For straight-line drawings of planar graphs with n vertices, the optimal worst-case bound on the area of a drawing is Θ(n²). The nested triangles graph requires this much area no matter how it is embedded, and several methods are known that can draw planar graphs with at most quadratic area.Binary trees, and trees of bounded degree more generally, have drawings with linear or near-linear area, depending on the drawing style. Every outerplanar graph has a straight-line outerplanar drawing with area subquadratic in its number of vertices, If bends or crossings are allowed, then outerplanar graphs have drawings with near-linear area. However, drawing series-parallel graphs requires an area larger than n by a superpolylogarithmic factor, even if edges can be drawn as polylines.

Area (band)

Area - International POPular Group, most commonly known as Area or AreA, is an Italian progressive rock, jazz fusion, electronic, experimental group formed in 1972 by singer Demetrio Stratos and drummer Giulio Capiozzo. They are considered one of the most respected and important bands of the blooming 1970s Italian progressive rock scene.

History

Demetrio Stratos' years: 1972–1979

Area were formed in Milan in 1972. Originally composed of Demetrio Stratos, Giulio Capiozzo (drums and percussion), Victor Edouard "Eddie" Busnello (saxophone and flutes), Leandro Gaetano (piano), and Johnny Lambizzi (guitar), soon followed by Patrick Djivas (bass) and Patrizio Fariselli (keyboards and piano). The band was led by Demetrio Stratos, an original and talented singer originally from Greece. In 1973, Johnny Lambizzi left the band and was replaced by Paolo Tofani (guitar and synth). In that year, they recorded their first studio album Arbeit macht frei ("Work Brings Freedom"), taken from the inscription that was found on the gate at the entrance to Auschwitz Nazi concentration camp, was released by Cramps Records and the band performed in many musical and cultural events. Area went on tour in Chile and, representing Italy, they took part in the eighth Biennale de Paris. At that time, Area's sound was an odd mish-mash that drew from rock, jazz, Eastern, and Arabic music, and it was the blending of all sorts of music that made the band stand out. The band soon grew to prominence because the youth of the time were able to identify with Area's socialist lyrics, and the band was founded on a strong and virtuosic musicianship. To aficionados of Italian progressive rock, their debut album Arbeit macht frei is considered a classic.

Area 30

Area 30 can refer to:

Heaven (BeBe & CeCe Winans album)

Heaven is the third album released by brother and sister duo BeBe & CeCe Winans and their second released on Capitol Records. It was number one on the Billboard Top Gospel Albums chart.

Smooth jazz musician Lonnie Liston Smith covered the title song from his 1990 album, Love Goddess

Destiny's Child singer Michelle Williams, featuring fellow singer Carl Thomas also covered the title song in the closing track from her 2002 solo debut, Heart to Yours.

Track listing

Charts

Singles

References

Heaven (Must Be There)

"Heaven (Must Be There)" (sometimes shortened to just "Heaven") is a song by Eurogliders from their album This Island. The song was released as a 7" vinyl and a 12" in May 1984.

The single brought the band to fame, especially in Australia, where the single peaked at No. 2 on Kent Music Report Singles Chart in 1984. It was also a major hit in New Zealand, peaking at No. 6, and a more modest hit in North America, hitting No. 47 in Canada, and No. 65 in the US.

Track listing

References

Heaven (Stewart and Cohen novel)

Heaven is a science fiction novel written by Ian Stewart and Jack Cohen. It was first published in 2004. It is a loose sequel to Wheelers.

Higher

Higher may refer to:

Education

Music

Songs