# Questions tagged [metrics]

The tag has no usage guidance.

25 questions
Filter by
Sorted by
Tagged with
39 views

### Approximate nearest neighbor search for $(\ell_p)^p$ metric, $0 < p < 1$

It is well known that approximate bichromatic nearest-neighbor search can be solved in sub-quadratic time for the $\ell_1$ and $\ell_2$ norms, as well as some other metrics. Are there any such results ...
36 views

45 views

### Fixed orientation metrics

I am currently working on some computational geometry problems with non-euclidean metrics, and have some trouble on a fact that sounds easy enough, at least intuitively. The fact is as follows: ...
119 views

### Quality measure for clusters of a metric space embedding of a graph?

When evaluating clustering algorithms for networks, we have well-established metrics like Modularity and Surprise for evaluating the quality of the resulting partition. If we then embed our graph (...
215 views

### Is “normalized distance” (as per Li & Vitanyi, Kolmogorov Complexity) a reasonable thing?

In "The Similarity Metric" (Li, Vitanyi, et. al) they define a normalized distance (or similarity distance) as a function $\Omega \times \Omega \to [0,1]$ which is both symmetric and satisfies the ...
798 views

### Axioms for Shortest Paths

Suppose we have an undirected weighted graph $G = (V, E, w)$ (with non-negative weights). Let us assume that all shortest paths in $G$ are unique. Suppose we have these $\binom{n}{2}$ paths (sequences ...
1k views

### A data structure for minimum dot product queries

Consider $\mathbb{R}^n$ equipped with the standard dot product $\langle \cdot, \cdot \rangle$ and $m$ vectors there: $v_1, v_2, \ldots, v_m$. We want to build a data structure that allows queries of ...
171 views

### Combinatorial algorithm for optimization over semimetric polytope

This question is motivated by the Leighton-Rao relaxation for SPARSEST-CUT. Suppose one wants to find a non-trivial semimetric over an $n$-point space that minimizes a certain linear functional. More ...
201 views

### Weighted Metric Graph: ratio of sum of wts of edges to the wt of MST

I am working on complete metric graph (V,d) where shortest distance is used as metric. The question is how large can be the ratio of the sum of weights of all edges to the weight of the MST (minimum ...
2k views

### Isometric embedding of L2 into L1

It is known that given an $n$-point subset of $\ell_2^d$ (that is, given $n$ points in ${\mathbb R}^d$ with Euclidean distance) it is possible to embed them isometrically in $\ell^{n\choose 2}_1$. ...
103 views

### Does kd-tree search look at more leaves in L1 than in Lmax ?

Dear theorists and experimenters, I find that kd-tree search looks at many more leaves in $L_1$ than in $L_{max}$ ($L_\infty$). Does anyone else see this ? If so, why ? (An $L_1$ simplex of volume 1 ...
342 views

### How to calculate this string-dissimilarity function efficiently?

Migrated from stackoverflow. Hello, I was looking for a string metric that have the property that moving around large blocks in a string won't affect the distance so much. So "helloworld" is close ...
Since the term is overloaded, a brief definition first. A poset is a set $X$ endowed with a partial order $\le$. Given two elements $a,b \in X$, we can define $x \vee y$ (join) as their least upper ...