Unanswered Questions
940 questions with no upvoted or accepted answers
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
1k
views
Alternative to Bloom filter for extreme parameters
A Bloom filter is a space-efficient probabilistic data structure to perform membership-tests on a set (see Wikipedia's page for a definition; I use the same notations below).
I am interested in a ...
- 391
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
1k
views
Find set of points with maximum distance inside given intervals?
Let $A$ be a set of $n$ closed intervals, $I_i$, with both extremes positive integers. Is there an efficient algorithm to find a set of $n$ points $P_i$, with $P_i \in I_i$, such that the minimum ...
CommunityBot
- 1
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
235
views
Optimizing order of graph reduction to minimize memory usage
Having extracted the data-flow in some rather large programs as directed, acyclic graphs, I'd now like to optimize the order of evaluation to minimze the maximum amount of memory used.
That is, given ...
- 22.6k
8
votes
2
answers
343
views
Maximum set cover with non-overlap
Let the universe be the set $U$ and a set of subsets $S$ be such that $\cup_{s \in S} s = U$. I am interested in computing the longest sequence of sets $s_1, ..., s_k$ such that:
$s_i \in S$ $\forall ...
- 7,603
7
votes
0
answers
175
views
Finding a rainbow independent set in a circle
Inside the interval $[0,1]$, there are $n^2$ intervals of $n$ different colors: $n$ intervals of each color. The intervals of each color are pairwise-disjoint. A rainbow independent set is a set of $n$...
- 6,277
7
votes
0
answers
1k
views
Understanding the Polyhedral Model
I am wondering at a high level the mathematics of the Polyhedral Model.
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of ...
- 2,315
7
votes
0
answers
213
views
Algorithms for curve construction
I am interested in algorithms that construct continuous curves between two points in such a way that minimizes an energy functional of the curve. What sort of algorithms are most used for such tasks?
...
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
6
votes
0
answers
52
views
How to find the minimum number of elements to distinguish several given sets?
Given $n$ distinct sets $S_1, S_2, \cdots, S_n$, how to find a set $X$ such that $X \cap S_1, X \cap S_2, \cdots, X \cap S_n$ are still distinct, and the size of $X$ is minimum?
For example, given $\{...
- 39.2k