StreamTable: An Area Proportional Visualization for Tables with Flowing Streams
DOI:
https://doi.org/10.57717/cgt.v3i1.24Abstract
Let T be a two-dimensional table with each cell weighted by a nonzero positive number. A StreamTable visualization of T represents the columns as non-overlapping vertical streams and the rows as horizontal bands such that the intersection between a stream and a band is a rectangle with area equal to the weight of the corresponding cell. To avoid large wiggle of the streams, it is desirable to keep the consecutive cells in a stream to be adjacent. The difference between the area of the bounding box containing the StreamTable and the sum of the weights of T is referred to as the excess area. We attempt to optimize various StreamTable aesthetics (e.g., minimizing excess area, or maximizing cell adjacencies in streams).
* If the row permutation is fixed and the row heights are given, then we give an O(rc)-time algorithm to optimize these aesthetics, where r and c are the number of rows and columns, respectively.
* If the row permutation is fixed but the row heights can be chosen, then we discuss a technique to compute a StreamTable with small area and required cell adjacencies by solving a quadratically- constrained quadratic program, followed by iterative improvements. If the row heights are restricted to be integers, then we prove the problem to be NP-hard.
* If the row permutations can be chosen, then we show that it is NP-hard to find a row permutation that optimizes the area or adjacency aesthetics.
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Copyright (c) 2024 Jared Albert Espenant, Debajyoti Mondal
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