Unanswered Questions
1,618 questions with no upvoted or accepted answers
39
votes
1
answer
3k
views
Is it NP-hard to fill up bins with minimum moves?
There are $n$ bins and $m$ type of balls.
The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$.
You start with $b_j$ balls of type $j$. Each ball of ...
CommunityBot
- 1
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 \...
23
votes
1
answer
570
views
Is finding a weight-balanced tree NP-hard?
In the following, we consider binary trees where only the leaves have weights.
Let $T$ be a binary tree and $W(T)$ be the sum of the weights of its leaves.
Let $T.l$ and $T.r$ be the left child and ...
CommunityBot
- 1
23
votes
1
answer
2k
views
Could min cut be easier than network flow?
Thanks to the max-flow min-cut theorem, we know that we can use any algorithm to compute a maximum flow in a network graph to compute a $(s,t)$-min-cut. Therefore, the complexity of computing a ...
CommunityBot
- 1
18
votes
0
answers
403
views
Is the two-color leapfrog problem in P?
My question is whether a specific decision problem is in P or not. It's straightforwardly in NP. The decision problem is a specific case of the general $k$-color leapfrog problem.
I can already show ...
- 798
14
votes
0
answers
270
views
What can be proven regarding the differences in power between unary ECMAScript regex functions and primitive recursive functions?
In 2014, inspired by Regex Golf, I started exploring, along with a mathematician going by the name teukon, what could be done in the unary domain in ECMAScript regex that went significantly beyond ...
- 241
13
votes
0
answers
448
views
Choosing a subset of binary variables to maximize the sum of the highest $K$
Consider the following problem:
Input:
integers $n > m > k$;
$n$ numbers $0 \leq p_1, \ldots, p_n \leq 1$;
$n$ numbers $r_1, \ldots, r_n$ where ($r_i \geq 0$).
Let $X_1,\dots,X_n$ be $n$ ...
- 231
12
votes
0
answers
260
views
Covering a complete graph with n copies of an arbitrary graph: NP-complete?
Given a complete graph $G$, an arbitrary graph $H$, and a positive
integer $n$, are there subgraphs $A_1,\dots,A_n$ of $G$ (not necessarily disjoint) such that
their union is $G$, and each of them ...
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
245
views
Minimum edge deletion partitioning of a planar graph
I'm interested in the time complexity of the following problem:
Given an undirected planar graph $G=(V,E)$ and a weight function $w:E \rightarrow \mathbb{Z}$ (so weights can be negative, too), color ...
CommunityBot
- 1
11
votes
0
answers
419
views
Proof of PCP theorem
I am reading the proof of PCP theorem in Proof Verication and Hardness of Approximation Problems. The following paragraph appears in section 3 (page 4), "Outline of the Proof of the Main Theorem".
...
CommunityBot
- 1
10
votes
1
answer
513
views
is $P_{CTC} = BPP_{path}$?
I think that these two classes should be the same, but I can't find any literature about this and have a limited background on the topic.
This is my reasoning, and I would like to know if (1) this is ...
CommunityBot
- 1
10
votes
0
answers
1k
views
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
0
answers
164
views
Complexity class for probabilistic approximation algorithms with bounded error
What's the name of a complexity class of
optimization problems that have
"bounded error probabilistic approximation algorithms"?
Bounded error probabilistic version of APX
(as BPP is bounded error ...
- 73.1k