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# Questions tagged [ds.algorithms]

Questions regarding well-defined instructions for completing a task, and relevant analysis in terms of time/memory/etc.

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### Is it possible to sort by only knowing the sign of pairwise sums?

I am currently thinking of how much structure one actually needs in order to be able to sort things at all. All comparison-based algorithms need a direct comparability, but are we able to remove this ...
174 views

### How many samples are needed to reconstruct a path?

Consider an input set of vertices $V$ and vertices $s,t\in V$. The goal is to learn some unknown shortest path from $s$ to $t$; the set of edges of the graph is hidden at first and there may be ...
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1 vote
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### Mapping of entire balls using Locality Sensitive Hashing (LSH)

LSH functions are useful for approximate nearest neighbor search. They are usually defined, for distance metric $d$ and $c>1$ as follows: A family of hash functions is $(r, cr, p_1, p_2)$-LSH ...
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### Is there a fast algorithm for inverting a sparse matrix?

I am doing research on a random-walk like problem. As a critical part of my solution, I need to invert a non-singular sparse matrix of size $n \times n$ and with $O(n)$ non-empty entries. I'm working ...
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### Determining how n-tuples are sorted as you search them?

I have a sorted list of $N$ n-tuples, but I do not know exactly how they were sorted. The person who sorted them did so by lexicographically ordering some permutation least-to-greatest. For example, ...
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### What is the hardest instance for the group isomorphism problem?

Two groups $(G,\cdot)$ and $(H, \times)$ are said to be isomorphic iff there exists a homomorphism from $G$ to $H$ which is bijective. The group isomorphism problem is as follows: given two groups, ...
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### How is SDP an extension of spectral algorithms?

In one of his lectures, Uri Feige described semidefinite programming (SDP) as ... an algorithmic technique that extends both linear programming and spectral algorithms. I know the basic ...
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1 vote
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### The SQ argument in Balazs Szorenyi's paper

I am asking about the proof in Theorem 5 (page 6) of this paper, http://www.inf.u-szeged.hu/~szorenyi/Cikkek/sq_d0_ext.pdf Quite a few things about this short argument seem unclear to me, Towards the ...
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