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The zigzag product was introduced by Reingold, Vadhan & Wigderson (2000). When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric logspace and logspace are equal ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
The trace of a triangle wave or a sawtooth wave is a zigzag. Pinking shears are designed to cut cloth or paper with a zigzag edge, to lessen fraying. [2] In sewing, a zigzag stitch is a machine stitch in a zigzag pattern. [3] The zigzag arch is an architectural embellishment used in Islamic, Byzantine, Norman and Romanesque architecture. [4] [5]
Therefore, a zig-zag product can also be used to construct families of expander graphs. If G is a ( n , d , λ 1 ) -graph and H is an ( m , d , λ 2 ) -graph, then the zig-zag product G H is a ( nm , d 2 , φ ( λ 1 , λ 2 )) -graph where φ has the following properties.
In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. [3] A contour map is a map illustrated with contour lines, for example a topographic map , which thus shows valleys and hills, and the steepness or gentleness of slopes. [ 4 ]
PINS earnings call for the period ending December 31, 2024. ... products, and users make up our Taste Graph, which is the foundation of our AI recommendation engines and is used to amplify the ...
This can be accomplished either by hitting the ball out of play while it is still in fair territory (a conventional home run) or by an inside-the-park home run. Barry Bonds holds the Major League Baseball home run record with 762. [a] He passed Hank Aaron, who hit 755, on August 7, 2007.
Bobby Lowe was the first MLB player to hit four home runs in a single game, doing so in 1894. In baseball, a home run occurs when the ball is hit in such a way that the batter is able to circle the bases and reach home safely in one play without any errors being committed by the defensive team in the process. In modern baseball, the feat is ...