Unanswered Questions
1,054 questions with no upvoted or accepted answers
19
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1
answer
1k
views
Why hasn't functional programming researched dynamic trees?
Dynamic trees play an important role in solving problems such as network flows, dynamic graphs, combinatorial problems ("Dynamic Trees in Practice" by Tarjan and Werneck) and recently merging ...
CommunityBot
- 1
12
votes
1
answer
5k
views
Finding the longest repeating subsequence
Given a string $s$, I would like to find the longest repeating (at least twice) subsequence. That is, I would like to find a string $w$ which is a subsequence (doesn't have to be a contiguous) of $s$ ...
- 280k
11
votes
0
answers
1k
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Alternative to Bloom filter for extreme parameters
A Bloom filter is a space-efficient probabilistic data structure to perform membership-tests on a set (see Wikipedia's page for a definition; I use the same notations below).
I am interested in a ...
- 391
10
votes
2
answers
2k
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Why is the complexity of negative-cycle-cancelling $O(V^2AUW)$?
We want to solve a minimal-cost-flow problem with a generic negative-cycle cancelling algorithm. That is, we start with a random valid flow, and then we do not pick any "good" negative cycles such as ...
CommunityBot
- 1
9
votes
0
answers
784
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How can the shortest traveling salesman tour be found in $O(2^n poly(n))$ time and less than exponential space?
I'm stuck on problem 9.4 from The Nature of Computation which reads:
Dynamic Salesman. A naive search algorithm for TSP takes $O(n!)$ time to check all tours. Use dynamic programming to reduce this ...
- 1,058
8
votes
0
answers
117
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Data Structures for Non-Orientable Manifolds
I am looking for a data structure to represent non-orientable manifolds (i.e. meshes like Moebius Strip, but without self-intersection). I will then implement other algorithms using this DS such as, ...
- 73.1k
8
votes
0
answers
2k
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Choosing potential function in amortized analysis
How should I think to choose the potential function in the amortized analysis?
More specifically are there techniques or tips for choosing optimal or good potential functions?
- 82.4k
8
votes
0
answers
647
views
Chained operations on sequences with two operators
Given a binary expresion tree, with addition and multiplication operations, how can we optimize it's evaluation?
Can we learn from matrix chain multiplication? A generalization of matrix chain ...
CommunityBot
- 1
8
votes
0
answers
383
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Worst-case sparse graphs for Hopcroft-Karp Algorithm
Of large sparse biparite graphs (say degree 4) with N verticies, roughly speaking, which of them cause the worst case running time of the Hopcroft-Karp algorithm? What is their general structure and ...
- 73.1k
8
votes
0
answers
587
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Predecessor query where the insertion order is known
Assume I want to insert elements $1$ to $n$ into a data structure exactly once, and perform predecessor queries while inserting these elements (so insert(x) and <...
CommunityBot
- 1
7
votes
0
answers
134
views
Is it possible to efficiently maintain a directed graph where nodes unreachable from the root are deleted?
I have an infinite set of possible nodes $V$ and a "root node" $r \in V$. I would like to maintain a directed graph with the invariant that all nodes in the graph are reachable from $r$. ...
- 195
7
votes
0
answers
353
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What was the first public reference to bloom filters where the number of hash functions vary?
In traditional bloom filters, each item is hashed some fixed number of locations. One variant of this is to hash items a varying number of locations within the same bloom filter.
This idea is ...
- 529
7
votes
0
answers
1k
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Double Hashing and Variations for Bloom Filters
I am reading a few papers on Bloom Filters – Bloom Filters in Probabilistic Verification (Dillinger and Manolios) suggests the following allocations for double and triple hashing respectively
$...
- 113
7
votes
0
answers
557
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What is the average-case running time of Fun-sort?
I read this paper: http://www.sciencedirect.com/science/article/pii/S0166218X04001131?np=y (you can check the PDF online for free), and I translated section 4's Fun-sort algorithm (correct me if I'm ...
- 1,090
7
votes
0
answers
203
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What is the proof for the lemma "For every iteration of the Gomory-Hu algorithm, there is a representant pair for each edge"?
For a given undirected graph $G$, a Gomory-Hu tree is a graph which has the same nodes as $G$, but its edges represent the minimal cut between each pair of nodes in $G$. The Gomory-Hu algorithm finds ...
- 22.6k