Unanswered Questions
799 questions with no upvoted or accepted answers
32
votes
1
answer
886
views
Largest set of cocircular points
Given $n$ points with integer coordinates in the plane, determine the maximum number of points that lie on the same circle (on its circumference, not its interior).
This can be done in $O(n^3)$ easily ...
CommunityBot
- 1
26
votes
1
answer
784
views
Complexity of deciding whether there is a winning strategy in the following game
The sum divider game for $n$ starts with the set $M_0 = \{1,\dots,n\}$. Player A chooses a number $m_1$ from $M_0 \setminus \{1\}$ and B has to choose a divider $m_2$ of $m_1$ from $M_1 = M_0 \...
10
votes
0
answers
1k
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Complexity of Sorting Integers on a Multitape Turing Machine
How expensive is sorting integers on a Multitape Turing Machine? Well known sorting algorithms, like quicksort, tend to rely on jumping / indirect-access being cheap. But MTMs have no indirect access.....
- 5,962
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
209
views
Complexity of frog game on graphs is exponential, or can we do better?
Frog game initializes by placing one frog on every vertex of a simple connected graph $G$ with $n$ vertices. A move consists of moving all $x\gt 0$ frogs from one vertex to another non-empty vertex to ...
- 117
9
votes
0
answers
372
views
P vs NP and the Time Hierarchy
Assuming $P\neq NP$, is it possible that there exists a $k$ such that $P\subseteq\textsf{NTIME}(t^k)$?
There reason I ask this is that I assume the following:
$$P=NP \implies \forall k\ \exists j.\ \...
CommunityBot
- 1
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
1k
views
Non-deterministic time hierarchy theorem: universal TM overhead
I am currently reading the book of Arora and Barak on computational complexity.
In the third chapter (p69-70), two classic theorems regarding time complexity hierarchies are introduced:
$\left[f(n)\...
- 81
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
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
172
views
Overlap Maximization problem
Here's the problem:
I have a collection of collections, $C$, where each $c\in C$ is a collection of sets $X\subset U$. Denote $c_i$ as the i-th $X$ in $c$. Informally, I want to map all the sets in ...
- 378
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
115
views
Polynomial time algorithms for graphs and cycles
For a given undirected graph $G$ , let $ c(G) $ denote the length of the longest cycle in $ G $ (by cycle, we mean a closed path without repetitions). Prove that if there exists a polynomial-time ...
- 7,603
6
votes
0
answers
1k
views
Time complexity of obtaining the support set of an unsorted sequence?
Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we can read, write and compare them in O(1) time with arbitrary positions). What's known ...
- 1,025
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