Questions tagged [greedy-algorithms]
Questions about algorithms that make at each step the locally optimal choice.
349
questions
0
votes
0answers
31 views
Sum optimization and greedy approach
I've came across the optimization bellow
$\phi=argmin_{\theta} \displaystyle\sum_{i=1}^{N}f(x_i,\theta)$
Can i say that minimizing this summation by minimizing each term $\left(\displaystyle\frac{df(...
0
votes
1answer
99 views
How to determine the approximation factor for greedy vertex cover algorithm?
The algorithm iteratively picks the vertex with maximum degree and removes it and every incident edge of the vertex, until only vertices with degree of $0$ are left.
Formally:
$\text{GreedyVertexCover}...
5
votes
0answers
49 views
Optimality of DSATUR on interval graphs
The DSATUR algorithm is a greedy graph coloring algorithm. It consists of applying the usual greedy coloring algorithm, considering vertices in reverse lexicographic order of (number of different ...
-1
votes
0answers
139 views
having n towers, find the max and min possible height for the longest tower after d days
I have faced this problem and can't find any similar question anywhere. Will you please help me solve it plz?
The question is for junior software engineer interview ...
1
vote
1answer
22 views
Minimal number of intervals that covers $\{1,…,k\}$
Let $F$ be a family of sets of consecutive integers in $\{1,…,k\}$ that is closed under taking subintervals, i.e. for any $a≤b≤c≤d$, if $\{a,…,d\} \in F$, then $\{b,…,c\} \in F$ also. Find a minimum ...
3
votes
0answers
28 views
Equalizing level of water in glasses problem
I have a problem on my hands, and would like help matching it to the existing, studied problems. I explain it like so:
I have a sequence of $n$ equal-sized glasses of water. Each has a different ...
-1
votes
1answer
32 views
Fitting arrays into RAM algorithm question
We'll consider the RAM as a sequence of cells that can contain data. Some cells already contain some data, some are empty. The empty cells form the so-called memory clusters. Thus, a memory cluster is ...
3
votes
1answer
122 views
Partition of a $k$-partite graph to minimal number of connected sets
Let $G$ be a $k$-partite directed acyclic graph where the edges are only between two adjacent sets of vertices.
I'm trying to partition the graph to the minimal number of connected sets.
Sets $A_0, ...
1
vote
0answers
45 views
Finding an optimal solution for the following problem
This is an intriguing question given by my friend for which I want to find an optimal solution:
Each week, you can choose to work ONLINE $(ON)$ or in person $(WR)$ in
your department's office. If you ...
0
votes
0answers
90 views
Minimum Number of Refueling Stops with Dynamic Programming
This is a question from Leetcode and I wanted to solve it with Dynamic Programming. upon seeing the solution, I am not able to get the intuition behind the logic. I was able to understand the solution ...
1
vote
0answers
20 views
Time to form a complete graph from n vertices given that only k vertices can be used at a time [closed]
I know this problem is related to the greedy algorithm and max edges incomplete graph but can't come up with a solution.
Problem
You are given two numbers n and k:
n >= k
n is the total # of ...
1
vote
1answer
84 views
How to prove the my greedy algorithm for placing guards?
Given $n$ images placed in indexes $x_1 < x_2 < ... < x_n$ and an endless number of guards, where each guard if placed in index $y$ can protect $[y-0.5,y+1]$. I want to protect all images ...
0
votes
0answers
37 views
Filling Two Knapsacks with greedy algorithm
I've got the next problem, where I have two, instead of one, knapsacks. Formally, we have items $1, \ldots , n$ and each item $i$ has a positive integer weight $w_i \in \mathbb{N}$ and a positive ...
1
vote
3answers
39 views
Greedy Algorithm: Optimal Substructure
I don't have a CS degree but I have recently taken up studying algorithms very seriously.
I have been studying greedy and dynamic programming for days and I come across the below definition a lot, ...
0
votes
0answers
24 views
Is correctness implied by an optimality proof?
New to proofs (in the context of analysis of algorithms).
I'm wondering, if I were to prove a greedy algorithm is the optimal solution, does this imply its correctness as well? (partial correctness + ...
0
votes
0answers
27 views
Proof of Correctness Request for Greedy Algorithm that solves “The Weight Job Scheduling” problem
Today, in my self-lead studies, I found out about greedy algorithms, more specifically, a greedy approach to solve The Weighted Job Scheduling Problem.
I understand how the solution is implemented but,...
1
vote
0answers
32 views
Which algorithms exhibits Greedy Choice Property but not Optimal Substructure Property
After a few courses using CLRS, I still have not been able to find a satisfying answer to the title question.
This answer suggests Hoffman trees. But here the greedy choice is the two subtrees with ...
-1
votes
1answer
100 views
Proof of Correctness : Arranging the sheep
I've come across a question in Codeforces contest 719(Div - 3).
The problem goes like this :
I was able to solve the problem by using another approach but had to use 4*n auxiliary space, where n is ...
0
votes
0answers
33 views
maximal independent set on grid-based graph proof of approximation ratio
We have a G = (V, E, w), in form of a grid graph with a single diagonal line in each grid in form of below. Where w is the V weight.
We use a greedy algorithm that takes in each step maximum weighted ...
2
votes
1answer
24 views
Optimize stacking time series by offsetting start times (feels like a backpack problem?)
Given a time-series of data collected from a single running process that takes 8 hours to complete:
Minute
GB of Disk Space Used
0
0
1
8
2
15
3
22
...Etc. It is sampled every minute, for 8 ...
1
vote
1answer
38 views
Find the minimum cost of adding the elements of a set (greedy algorithm)
I'm VERY stuck with this problem:
Given a set (with possible repeated elements), the cost of adding two elements $x, y$ is $x + y$.
For example, the possible costs of the next set $\{1,2,5 \}$ are:
...
3
votes
1answer
45 views
Expected behavior of an algorithm to minimize rankings
Suppose $n$ students have preferences over $n$ different notebooks. Their preferences can be represented with a square matrix of size $n$ where each column is a different permutation of the vector $[1:...
1
vote
1answer
25 views
Greedy approach suggestions for assigning objects
Suppose there are three categories of people.
Type X, Type Y, Type Z.
In each type, there are two objects of subtype Type 'a' and type 'b'.
For example.
X: a1 , a2 , b1 , b2
Y: a3 , a4 , b3 , b4
Z: a5 ...
2
votes
1answer
45 views
k-center problem: proof for Gon algorithm gives a 2-approximation
The $k$-center problem is where we a given a graph $G(V,E)$, an integer $k$, a distance metric $d$ and we want to find a subset $C\subseteq V$ (such that $|C|\leq k$) which minimizes the following ...
1
vote
1answer
78 views
Find minimum number of points which intersect overlapping arcs
Say I have a circle of a fixed radius, with overlapping arc intervals along its edge. I want to return a minimum set of Points which intersects all arcs in $n^2$ time.
I'm having some trouble proving ...
1
vote
1answer
34 views
Does any graph based optimization problem, which have a greedy algorithm, has guarantee that there exist an order which give the optimum
There exist greedy algorithms for vertex coloring like optimization problems. We know that for graph coloring, there is an order of vertices for which greedy coloring produces the optimum results. Is ...
0
votes
1answer
33 views
A problem about Huffman codeword
Under Huffman Encoding, what circumstances codeword length of each character
be equal?(suppose number of character is power of 2)
I think if all frequency of characters is same then codeword length ...
1
vote
1answer
63 views
Greedy algorithm for maintaining drugs
Given $n$ drugs such that each drug $d_i$ should maintain in interval
$[c_i,h_i]$.We want to minimize number of containers to maintain
medicines in compatible interval.
My answer is as follows:
I use ...
2
votes
1answer
13 views
Scheduling algorithm for a student's study times given assignments, expected time, due dates, and class times
I would like to create an algorithm that advises a student when they should work on certain assignments given the expected time each assignment will take, and the due date of each assignment.
Say that ...
4
votes
1answer
127 views
Hamiltonian path greedy and anti-greedy algorithms
I had this question on a problem set recently, but I wasn't sure how to solve it.
Given a complete weighted undirected graph $G$, here are two "algorithms" to find a Hamiltonian path:
...
0
votes
0answers
89 views
Finding name of a specific problem
Input : $x \in \mathbb Z$ and $a_1,a_2,\dots,a_n \in \mathbb N$.
Output : $b_1,b_2,\dots,b_n \in \mathbb Z$ such that $\sum_{i} a_i b_i=x$ and $\sum_{i}|b_i|$ is minimized.
Main question is, can we ...
0
votes
0answers
54 views
Need help with a very specific Greedy Algorithm. Are there fast solutions?
i need help for a specific problem i have at work.
You have N number of rows in an array, each with some distribution of Numbers that range from 0 to N.Given an array of size 1000:
Row 1 might look ...
0
votes
0answers
29 views
Minimum cost bin assignment
I've been trying to solve the below problem the entire day but couldn't come up with a solution. I have the suspicion that it could by solved by a graph algorithm (or maybe some greedy approach?) but ...
1
vote
1answer
34 views
Must an optimization problem with a greedy algorithm belong to P?
If it is known that for some optimization problem there is a greedy algorithm that solves it and the solution includes sorting of input at the preliminary stage, is it necessarily true that the ...
1
vote
2answers
71 views
Best approach to resource allocation problem
Problem
The enemy army has taken $n$ of our cities. In each city $i$ the enemy has placed $e_i$ soldiers. We have $n$ teams, each team $j$ with $d_j$ soldiers. If we place more soldiers in a city ...
0
votes
1answer
27 views
Algorithm of split graph $G=(V,E)$ to 2 groups that at least half of the edges are between the groups [duplicate]
Can someone remind me the algorithm that split vertex of graph to 2 groups that at least half of the edges are external, I mean between the groups. As I remember it was a greedy algorithm, each time ...
0
votes
1answer
61 views
What Makes an Algorthim Greedy [Graph Coloring Algorithm]
I have a simple graph G = (V,E) and each vertex has a range [a,b].Every two vertices are connected only if [a_1,b_1] and [a_2,b_2] have a common subrange.
Each range of vertex is rV1 = [0,5] rV2 = [1,...
4
votes
1answer
55 views
Is the following Greedy algorithm to generate Gray Codes always correct?
I recently solved the basic problem of generating a n-bit Gray Code. The solution I used involved building larger-bit Gray Codes from smaller ones recursively (the solution I've seen on most websites)....
2
votes
2answers
89 views
Maximize number of subsets
Given a list of subsets $S_1, \ldots, S_n$ of the universal set $U = \{e_1,\ldots, e_m\}$, find a subset $S \subset U$ of size $k$ that contains the maximum number of subsets $S_i$. In another words,
$...
0
votes
1answer
77 views
How to (Efficiently) Sort a List of Items with Parent/Child Relationship
I have a list of items that have a parent/child/grandchild/etc. type of relationship. Each item has a list of descendants, and an _.isDescendentOf(other) member ...
1
vote
1answer
45 views
Maximum Independent Set of special Directed Graph
I was given this special type of Directed Graph and was asked to find it's Maximum Independent Set.
Graph Properties :
Graph has $N$ vertices and $N$ edges
There can be no edge from a vertex $v$ to ...
3
votes
1answer
125 views
Greedy algorithm for subset sum on powers of 2
I have some $n$ numbers which are powers of $2$, say $a_1,a_2,a_3,\ldots,a_n$ which are not necessarily all distinct. I have option to give them any sign. I have to find if I can make their sum after ...
0
votes
0answers
27 views
Rearrange string k distance Apart
The question statement is as follows:
Given a non-empty string s and an integer k, rearrange the string such that the same characters are at least distance k from each other. All input strings are ...
1
vote
0answers
19 views
Greedy Best-First Search Performance for Tree and Graph Space
I am currently reviewing the GBFS algorithm and when looking at its completeness I am confused between the difference of it being
not optimal in Tree Search for Finite and Infinite Spaces
that it is ...
3
votes
0answers
18 views
Spanning hypertree which connects the vertices as slowly as possible
I want to find a reference for the following problem or a similar problem for my paper. I found a greedy algorithm for this problem, but writing such an algorithm in a paper is not common in my area, ...
0
votes
2answers
53 views
Highest Product of X Items
🧩 How do you find the highest product of X items?
This should optimize for runtime complexity and protect from overflows from large products.
Inputs
An array of both positive and negative Ints ...
2
votes
1answer
55 views
2-Approximation algorithm for for messages across a cyclic network
Question
There are $n$ computers arranged in a cycle ($1,2,3..,n,1$), with undirected edges between adjacent computers. There are $m$ messages that need to be delivered. Message $i$ ($1 \le i \le m$) ...
2
votes
1answer
33 views
Modified topological sort
I recently asked a related question at the theoretical CS stack exchange, but I have modification to the problem that I think is a bit tougher. This seems like a better place anyways.
Let's define a &...
1
vote
0answers
33 views
Does the existence of a matroid structure imply that the greedy algorithm is optimal?
I was going through the topic of matroid structures for the problems like Activity selection ,minimum spanning tree. I also came to know how to solve if a problem exhibits matroid structure. The ...
0
votes
0answers
30 views
Greedy Proof: For coin denomination systems, faster proof to ensure greedy solution yields the optimal solution
I have reasons to believe that there is a faster way to confirm, that for coin denomination systems if the greedy solution yields the optimal solution or not.
I believe that if you check that for all ...
