Unanswered Questions
765 questions with no upvoted or accepted answers
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
10
votes
2
answers
2k
views
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
views
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
9
votes
0
answers
228
views
How to solve the loan graph problem
The problem
A loan graph is a directed weighted graph $\mathcal{G} = (V, A),$ where $A \subseteq V \times V.$ If we have a directed arc $(u, v)$, we interpret it as the node $u$ gave a loan of $w(u, ...
- 52
8
votes
0
answers
224
views
Formulating shortest path as submodular minimization
I'm curious about the general question of whether any combinatorial optimization problem with polynomial time solution can necessarily be reformulated as minimizing a submodular function.
The answer ...
- 113
8
votes
0
answers
2k
views
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
views
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
7
votes
0
answers
203
views
Number of strings at given edit distance
I would like to know the number of strings at edit distance $n$ of a string $s$.
I guess this is textbook knowledge... but I cannot find the textbook in question.
More formally, I have an alphabet $\...
- 8,372
7
votes
0
answers
697
views
Algorithms to generate random nowhere-neat rectangulation?
I want to generate random rectangular partition of a given $m*n$ rectangle under the constraint that it must be nowhere-neat partition. Nowhere-neat partition means that a dissection of a rectangle ...
- 4,467
7
votes
0
answers
557
views
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
views
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
6
votes
0
answers
97
views
Scheduling tasks on a graph with assistance
This is a follow-up to a question that I recently posted here: Completing tasks on a graph. In that question, I posted the following:
Consider a graph $G = (V, E)$, where $V = \{0, 1, 2, \ldots, n\}$. ...
CommunityBot
- 1
6
votes
0
answers
292
views
Is greedy minimax permutation rejecting sorting optimal?
I sketch an impractical, theoretical comparison sort.
Initialize a list of all $n!$ permutations of size $n$.
For each possible pair of indices $i, j$, count how many permutations would get rejected ...
- 73.1k
6
votes
0
answers
224
views
Upper bound on the number of hamiltonian cycles on a $n \times n $ grid graph
What is the best upper bound that is known for the number of hamiltonian cycles on a $n \times n $ grid graph?
I did some searching and found that the number of hamiltonian cycles on a planar graph ...
D.W.♦
- 167k