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-1
votes
0answers
40 views

Developing Matrix Chain Multiplication Algorithm [closed]

Supposing, we don't know the DP algorithm for MCM. What could be the line of thought, that will lead us to the solution?(or develop it) Starting with the brute force method, we can examine all ...
-2
votes
1answer
73 views

Liner time complexity for wordwrap problem

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/
5
votes
0answers
109 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
120 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
56 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?
1
vote
4answers
196 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
385 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.
1
vote
0answers
101 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
402 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 ...
4
votes
0answers
147 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) ...
4
votes
1answer
332 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 ...
2
votes
1answer
133 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
236 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 ...
1
vote
0answers
268 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
443 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 ...
24
votes
0answers
909 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 $\{0,1,\ldots,n+1\}$. ...
37
votes
0answers
741 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 ...
7
votes
1answer
281 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 ...
1
vote
0answers
320 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
856 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
329 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 ...
6
votes
0answers
247 views

Embedded dynamic programming (and planar subgraph isomorphism)

In Planar Subgraph Isomorphism Revisited, Frederic Dorn obtains an improved algorithm for Planar Subgraph Isomorphism, by using a technique he calls Embedded Dynamic Programming. This technique ...
0
votes
1answer
259 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 ...