l1-Embeddability Under Gate-Sum Operation of Two l1-Graphs

Overcoming the l1 non-embeddability barrier: algorithms for product metrics

A common approach for solving computational problems over a difficult metric space is to embed the “hard” metric into L1, which admits efficient algorithms and is thus considered an “easy” metric. This approach has proved successful or partially successful for important spaces such as the edit distance, but it also has inherent limitations: it is provably impossible to go below certain approxim...

The cut cone, L1 embeddability, complexity, and multicommodity flows

A finite metric (or more properly semimetric) on n points is a non-negative vector d = (dij) 1 ≤ i < j ≤ n that satisfies the triangle inequality: dij ≤ dik + d jk . The L (or Manhattan )distance | |x − y| |1 between two vectors x = (xi) and y = (yi) in R is given by | |x − y| |1 = 1≤i≤m Σ |xi − yi |. A metric d is L − embeddable if there exist vectors z1, z2, . . . , zn in R for some m, such t...

Bounds on the sum of L1 influences

Let f : {−1, 1}n → [−1, 1] have degree d as a multilinear polynomial. It is well-known that the total influence of f is at most d. Aaronson and Ambainis asked whether the total L1 influence of f can also be bounded as a function of d. Bačkurs and Bavarian answered this question in the affirmative, providing a bound of O(d) for general functions and O(d) for homogeneous functions. We improve on ...

Cuts, Trees and l1-Embeddings of Graphs

L1 Glossing and Lexical Inferencing: Evaluation of the Overarching Issue of L1 Lexicalization

This empirical study reports on a cross-linguistic analysis of the overarching issue of L1 lexicalization regarding two (non)-interventionist approaches to vocabulary teaching. Participants were seventy four juniors at the Islamic Azad University, Roudehen Branch in Tehran. The investigation pursued (i) the impact of the provided (non)-interventionist treatments on both sets of (non)-lexicalize...