Questions tagged [dynamic-programming]
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51
questions
1
vote
0answers
80 views
How to approach the “traveling salesman problem” with cost changing every time salesman reaches a new city
Let's say instead of finding the shortest path we have to maximize the profit in a year of the salesman under the following constraints.
Salesman can go to a different city only on weekends, all ...
0
votes
0answers
47 views
choosing the best subset where the metric is based on pairwise relationship
I want to model the competition between agents.
Say there is a set of agents, and at each time step each agent $i \in \{0,1,\cdots, n-1\}$ can select a nonnegative number $x_i$ from a given range $[0,...
2
votes
0answers
206 views
Run Length eXtreme encoded length
In run length encoding (RLE) the code stream consists of pairs $(c_i,\ell_i)$, which is understood as writing the character $c_i$ repeatedly $\ell_i$ times.
Consider the following "improvement" of ...
2
votes
1answer
84 views
Longest stack-sortable subsequence
Given an array of $n$ pairwise-different positive integers, the problem is to find the longest subsequence that is stack-sortable, i.e. avoiding the permutation pattern $231$.
How fast can this ...
1
vote
1answer
135 views
A dominate vector subset sum problem
Let $k$ be some constants (e.g. one can take $k=2$ for simplexity), for any $u,v\in \mathbb{R}$, we say $u$ dominate $v$ if $\forall 1\le i\le k,~ u[i]\ge v[i]$, write it as $u\succ v$.
Consider the ...
-4
votes
1answer
91 views
Ordering of sub problems in dynamic programming
1) Can every dynamic programming question be solved using 3 different orderings or can there be more than 3 or less than 3 ( like unique ordering )?
My understanding is that a) it might have a unique ...
1
vote
1answer
182 views
How can I rank paths through an HMM? [closed]
I have a profile hidden Markov model that I use to identify all instances of a user-defined pattern of symbols in a long sequence of symbols. I use the Viterbi algorithm to find the most probable path ...
-1
votes
1answer
306 views
Duration Viterbi Algorithm
I am searching for some good resources to understand the Duration Viterbi algorithm.
Does anyone knows a good resource to understand and learn how to model a Duration Viterbi Hidden Markov Chain ...
2
votes
0answers
54 views
Probabilistic linebreaking algorithm
I'm currently trying to implement this paper:
Bouckaert, Remco R., A probabilistic line breaking algorithm, Gedeon, Tamás D. (ed.) et al., AI 2003: Advances in Artificial Intelligence. 16th ...
30
votes
0answers
4k views
Combinatorics of Bellman-Ford or how to make cyclic graphs acyclic?
Roughly speaking, my question is:
How costly is to make a cyclic graph
acyclic while preserving all simple $s$-$t$ paths?
Let $K_n$ be a complete undirected graph on vertices $\{0,1,\ldots,n+1\}$.
(...
5
votes
3answers
448 views
Beating naive dynamic programming: examples similar to integer partitions?
Let $p(n)$ denote the number of partitions of $n\in\mathbb{N}$ (briefly, number of ways to split a pile of $n$ stones into $\geq1$ unordered nonempty parts). The classical dynamic programming ...
5
votes
0answers
68 views
Series-parallel extension of a partial order respecting a given total order
Consider a partial order $P$, a series-parallel order $Q$ and a total order $R$, such that $P \subseteq Q \subseteq R$. Given $P$ and $R$, we are asked to find $Q$ of minimum length.
An $O(n^3)$ ...
2
votes
0answers
104 views
Is scalable hardware support for LogCFL (= sAC^1) possible?
The (uniform) circuit classes $TC^0$, $NC^1$ and $sAC^1$ seem to lend themselves to efficient hardware implementation. But using an FPGA approach to create the circuits on the fly seems problematic, ...
1
vote
1answer
205 views
Max weight travel on a graph with deadline
Given a deadline $D>0$ and a complete graph $K_n$ (with loops) in which each edge $e_{ij}$ has a weight $w(e_{ij}) \ge 0$ and a travel time $l(e_{ij}) > 0$. Starting from one of the nodes, we ...
1
vote
0answers
49 views
Counting multiplicative closures
Given a set $S$, its multiplicative closure is the set
$$
\mathcal{M}(S) = \{s_1s_2\cdots s_k: k\in\mathbb{N},s_i\in S\}
$$
of products of zero or more elements of $S$. So the multiplicative closure ...
9
votes
0answers
477 views
How to prove “obvious” facts?
The title is somewhat "arrogant": say, most of us treat $P\neq NP$ as an "obvious" fact, albeit no proof is in sight. But my question is at a much, much lower level, is about a fact which "should be" ...
2
votes
0answers
151 views
Paper regarding the complexity of the longest path problem on weighted directed graphs of bounded treewidth
I would like to cite a paper/report/etc that solves the following problem polynomially in $n$:
Given a weighted directed graph $G=(V,E)$, $|V|=n$, of bounded treewidth $k \in \mathbb{N}$ and a source-...
10
votes
0answers
272 views
Monotone circuit complexity of matroids?
Call a monotone boolean function $f$ a matroid function if its minterms are bases of some matroid.
I am interested in monotone circuit complexity of such functions, even when we "tie hands" of these ...
16
votes
0answers
447 views
Can short-distance connectivity be harder than connectivity?
Has anybody seen the following (or similar) question being considered:
Can it be easier to determine the presence/absence of $s$-$t$ paths than to determine the
presence/absence of short $s$-$t$ ...
-1
votes
2answers
3k views
Dynamic Programming vs Greedy Algorithm
In (Sniedovich 2006) "Dijkstra's algorithm revisited: the dynamic programming connexion", Sniedovich provides us another interpretation of Dijkstra's algorithm as a dynamic programming implementation. ...
14
votes
1answer
817 views
Monotone arithmetic circuit complexity of elementary symmetric polynomials?
The $k$-th elementary symmetric polynomial $S_k^n(x_1,\ldots,x_n)$ is the sum of all $\binom{n}{k}$ products of $k$ distinct variables.
I am interested in the monotone arithmetic $(+,\times)$ circuit ...
15
votes
1answer
618 views
Is Dynamic Programming never weaker than Greedy?
In the circuit complexity, we have separations between powers of various circuit models.
In the proof complexity, we have separations between powers of various proof systems.
But in the algorithmic,...
12
votes
1answer
364 views
Covering string by palindromes
Given a string $w=\sigma_1\sigma_2\ldots\sigma_n$, a palindrome cover is a sequence $p_1p_2\cdots p_m$ of words $p_i$ such that $p_1p_2\cdots p_m = w$ and such that each $p_i$ is a palindrome.
How ...
5
votes
0answers
137 views
Counting words of length $n$ in an inherently ambiguous CFG?
There is a polynomial-time algorithm for computing the number of words of length $n$ in an unambiguous CFG $G = (V, \Sigma, R, S)$ (via a dynamic programming approach). However, for ambiguous CFGs, ...
1
vote
0answers
24 views
Which matrix of Q values is being used here?
This question refers to this paper: Using Free Energies to Represent Q-values in a Multiagent Reinforcement Learning Task
In section 2.1, equations (5) and (6), I am wondering which Q values are ...
4
votes
0answers
158 views
What is the current “state-of-the-art” solver for quadratic knapsack problems?
New to this forum, so please let me know if my question format is incorrect.
For linear KP with $n$ items and $c$ capacity, dynamic programming can find exact solutions in $\mathcal{O}(nc)$. I have ...
0
votes
0answers
1k views
How to solve such a graph optimization problem?
I have a graph optimization problem which is hard to describe in the title.
There is a component based system which consists of components and data transmissions between components(components and ...
11
votes
0answers
323 views
a geometric variant of k-medians. NP-hard or in P?
The following problem is a special case of k-medians. Is it NP-hard? Is it in P?
Input: $n$ points $(x_1,y_1), (x_2,y_2), \ldots, (x_n, y_n)$ with each $y_i \ge 0$, and an integer $k$.
Output: a ...
5
votes
1answer
423 views
Long Cycle in Bounded Tree-Width Graphs using DFS and Dynamic Programming
For fixed parameter $k$, I would like to find a long cycle of length $\geq k$ in an undirected graph $G(V,E)$. This can be done in $O(k!2^k|V|)$-time [2] using 1) depth-first search (DFS) and 2) ...
3
votes
1answer
110 views
Locally sorted sequences
Let $S=s_1,\ldots,s_n$ be a sequence and $p$ be a permutation on the indices of $S$ such that $p$ sorts $S$.
Define a sequence to be locally sorted with degree $k$ if $\forall s_i \in S |p(i) - i | \...
1
vote
0answers
216 views
Dynamic Programming with two optimization goals
I am working on the problem of distributed database query planning. Existing work [1] uses dynamic programming to search the potential query plan space and find the one with minimal cost. However, I ...
-2
votes
1answer
836 views
Liner time complexity for wordwrap problem [closed]
Can some body explain me how to apply memoization technique to achieve linear time complexity for bellow.
http://www.geeksforgeeks.org/dynamic-programming-set-18-word-wrap/
45
votes
0answers
1k views
Monotone complexity of s-t connectivity
In the problem CONN, we obtain a directed $n$-vertex graph (encoded as a boolean string of $n^2$ bits, one for each potential edge), and want to decide
whether there is a path between all $n^2$ pairs $...
5
votes
0answers
145 views
Evidence of non P-hard problems that require polynomial space?
It is admitted that a $\mathsf{P}$-complete problem requires polynomial space and thus cannot be efficiently parallelized. One purpose of these problems is that they can be used to 'defeat' an (...
0
votes
0answers
196 views
Calculating exact/approximate solution to a formula
Suppose we have a set of variable $\mathbf{y} = \left(y_1, ..., y_n \right)$. Also consider the set of functions $g_i(y_i), 1 \leq i \leq n$. Note that $g_i()$ is dependent only on $y_i$.
Consider ...
4
votes
1answer
79 views
Bellman principle and approximability
Does anybody know if a combinatorial optimzation problem that enjoys the Bellman's optimality principle can in automatic way be approximated?
4
votes
1answer
354 views
Problem understanding “connectivity” characteristic for the $k$-connected subgraph problem
I am reading this article, and I am having trouble to understand the 11th definition (page 7) about the connectivity characteristic. I do understand the raw ...
1
vote
4answers
210 views
Efficiently generate list of lightest intervals of a vector
Suppose a vector of size $n$ is given. The goal is to compute, $\forall i \in [n]$ the lightest interval of size $i$ (i.e. the interval whose sum is minimal).
For example, if we have the array:
<...
-6
votes
1answer
2k views
Dynamic programming and Divide and conquer approach [closed]
How does Dynamic Programming differ from Divide and conquer approach for solving problems?
Can anyone explain the essential idea of Dynamic Programming.
Thanks for any help.
2
votes
0answers
387 views
extension for Levenshtein distance
I am looking for an extension for Levenshtein distance (Edit distance) for multi dimensional strings (2D and 3D). I am not sure if there is a formal definition for multi dimensional or not, but here ...
6
votes
0answers
1k views
Euclidean TSP algorithms
Are there any known exact algorithms for Euclidean TSP that take advantage of the inherent structure of the problem? Do any of these algorithms have better asymptotics than $O(2^n n^2)$ of a DP ...
2
votes
1answer
144 views
Computing unique subset intersections
Given a set S = {si : {zj : z ∈ N} }, what is a time-efficient algorithm for computing the unique sets of intersections of all of the subsets of S?
As per @JeffE's comment below, there are edge ...
3
votes
2answers
282 views
Find two sequences of integers that have sum N but that don't have sub-sequences starting at the head of equal sum
This question arose from a discussion between a friend and I.
$A$ is a sequence of length $T$ where for any $a_i$ in $A$, $a_i \in \left\{{1, 2, 3}\right\}$
$B$ is a sequence of length $U$ where ...
2
votes
0answers
399 views
How can I find all numbers for which the XOR-sum is 0?
Given a list of integers $[a_1, a_2, \dots a_n]$, I want to find the number of $n$-tuples $(x_1,\dots,x_n)$ of integers such that the following three conditions are satisfied:
$x_1 \oplus x_2 \oplus \...
8
votes
2answers
877 views
Is there some mathematical closed form (or somewhat tight asymptotic one) for “Google Eggs Puzzle”?
The following brief description of the known "Google Eggs Puzzle" comes mainly from the web site Google Eggs:
Google Eggs Puzzle: Given n floors and m eggs, what is the approach to find the highest ...
7
votes
1answer
416 views
Does this bin packing problem have a name?
My problem is related to the standard bin packing problem (where you have bins of capacity $1$, items of capacity $(0,1]$, and want to pack the items into as few bins as possible), but there are a ...
0
votes
1answer
284 views
Variable profit knapsack [closed]
sorry for bad formatting earlier
We are given Cx,i, Cy,i, Cz,i ∈ ℕ and Px,i, Py,i, Pz,i > 0 for i=1,2,3 such that Px,1 < Px,2 < Px,3, Py,1 < Py,2 < Py,3, and Pz,1 < Pz,2 < Pz,3. We ...
1
vote
0answers
478 views
Converting a bounded knapsack problem to 0/1 knapsack problem
I originally posted this question at the programmers section of StackExchange (because that section is supposed to deal with data structures and algorithms), but they suggested posting in the math ...
3
votes
2answers
2k views
Dynamic programming and shortest path problem
Several months back, I asked in math.SE the following question
I wonder if any dynamic programming problem can always be converted to
a source-sink shortest path problem in a network with source ...
1
vote
0answers
397 views
Cannot understand the problem of Bitonic Euclidean Traveling-Salesman [closed]
I am referring to the problem in Introduction to Algorithms. I kind of fail to understand the problem.
From what I see, I need to sort the x-coordinates of the given set of points and then form a ...
