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- W3136017044 abstract "We give a new randomized algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into R2 Cartesian space preserving their l∞ (or l1) metric distances. Our expected time is O(n2 log3n) (i.e. within a poly-log of the size of the input) beating the previous O(n3) algorithm. In contrast, we prove that detecting l3∞ embeddings is NP-complete. The problem is also NP-complete within l21 or l2∞ with the added constraint that the locations of two of the points are given or alternatively that the two dimension are curved into a 3-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded in l3∞, however, can be if even one point is removed." @default.
- W3136017044 created "2021-03-29" @default.
- W3136017044 creator A5038153586 @default.
- W3136017044 date "2007-01-07" @default.
- W3136017044 modified "2023-09-28" @default.
- W3136017044 title "Embedding into l2∞ is easy embedding into l2∞ is NP-complete" @default.
- W3136017044 doi "https://doi.org/10.5555/1283383.1283439" @default.
- W3136017044 hasPublicationYear "2007" @default.
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