Unanswered Questions
3,056 questions with no upvoted or accepted answers
40
votes
1
answer
844
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 $P$ ...
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
25
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
- 1
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
18
votes
3
answers
1k
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
742
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
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
0
answers
236
views
Can you multiply complex 2x2 matrices in fewer than 21 real multiplies?
It is well known that 2x2 matrices can be multiplied using just 7 (instead of the obvious 8) multiplications in the ground field (Strassen-Winograd, etc.). It is also well known that complex numbers ...
- 201
12
votes
0
answers
956
views
Optimal meeting point in directed graph
Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$.
I need ...
- 238
12
votes
0
answers
835
views
Fast algorithm for max-convolution with concave functions?
I'm interested in a discrete max-convolution problem, which is to compute
$$r(c) = \max_{x | x \ge 0, \sum_k x_k = c} \left[ \sum_{k=1} f_k(x_k) \right] $$
for all values $c=0, \ldots, C$, where $x=(...
- 73.1k
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
388
views
Change in the distances in a graph after removal of a node
Given an undirected unweighted graph $G=(V,E)$ and a node $s \in V$, we are looking for a vector $\operatorname{diff}[]$, such that,
$$\operatorname{diff}[v] = \sum_{u \in V \setminus \{v\}}{(d^{G \...
- 1,944
10
votes
1
answer
479
views
Shift-resolve parsing - questions
I've recently came across a paper describing the parsing technique
mentioned in the title. Unfortunately, the terminology used in said paper
is somewhat beyond my comprehension, so I've been ...
CommunityBot
- 1
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
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