Unanswered Questions
10,291 questions with no upvoted or accepted answers
37
votes
0
answers
647
views
Finding an $st$-path in a planar graph which is adjacent to the fewest number of faces
I am curious whether the following problems has been studied before, but wasn't able to find any papers about it:
Given a planar graph $G$, and two vertices $s$ and $t$, find an
$s$-$t$ path $P$ ...
- 2,245
37
votes
1
answer
2k
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
30
votes
0
answers
769
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 $O(n^3)$ ...
- 2,245
24
votes
1
answer
1k
views
Compression of domain names
I am curious as to how one might very compactly compress the domain of an arbitrary IDN hostname (as defined by RFC5890) and suspect this could become an interesting challenge. A Unicode host or ...
CommunityBot
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23
votes
0
answers
1k
views
Can a calculus have incremental copying and closed scopes?
A few days ago, I proposed the Abstract Calculus, a minimal untyped language that is very similar to the Lambda Calculus, except for the main difference that substitutions are ...
- 71.9k
21
votes
0
answers
687
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 \...
- 133
20
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
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19
votes
0
answers
478
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 ...
- 22.1k
19
votes
1
answer
975
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
17
votes
0
answers
352
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 ...
- 758
16
votes
2
answers
801
views
Steps that guarantee exiting a maze
Given a 2-dimensional maze where you can give 4 commands "move up/down/right/left". Knowing the maze but not where the person is, how to find the minimum sequence of commands that guarantees exiting ...
CommunityBot
- 1
15
votes
0
answers
299
views
Using logic to prove non-regularity of a language
A language $L$ is regular if and only if it is definiable by a sentence in monadic second order logic (MSO) over strings (J.R. Buchi, Weak second-order arithmetic and Finite automata; Z. Math. Logik ...
- 71.9k
14
votes
0
answers
218
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
14
votes
0
answers
691
views
Test whether two languages are equal, when give in algebraic form
This sub-problem is motivated by Algorithm to test whether a language is regular.
Suppose we have two languages $L_1,L_2$ that are expressed in "algebraic" form, as formalized below. I want to ...
CommunityBot
- 1
13
votes
2
answers
1k
views
Flow graph that requires pushing back flow in Ford Fulkerson
Does there exist a flow graph that always requires flow to be pushed back no matter what ordering of augmenting paths is chosen in Ford Fulkerson?
Let's assume we use the standard procedure of ...
CommunityBot
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