Questions tagged [greedy-algorithms]
Questions about algorithms that make at each step the locally optimal choice.
319
questions
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
26 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
1answer
56 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,...
1
vote
2answers
53 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
23 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 ...
2
votes
2answers
82 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,
$...
4
votes
1answer
40 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
1answer
339 views
Going deeper with pseudo-polynomial time algorithm for set partitioning
If I have a set of (edit) positive integers, and I'm sure that the pseudo-polynomial time algorithm for partitioning the problem will not give me an answer - what would I do next?
To illustrate this ...
0
votes
1answer
20 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
40 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 ...
2
votes
1answer
368 views
Task Distribution Algorithm
Different machine has different efficiency on different tasks, like:
...
1
vote
2answers
299 views
FInding the combination with the least number of elements from and array of integers, given an integer sum
I'm doing and assignment where the problem is to find the combination with the least number of elements form an array of integers, given an integer sum. I have solved this using a gready algorithm ...
3
votes
1answer
74 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
17 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
18 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 ...
4
votes
1answer
292 views
An algorithm for a minimization problem, How to minimize the wasted length of combination of multiple items with different length and number
Suppose there is an unlimited number of pipes, each has length $x$ meters.
There is a list of requirements of pipes with shorter length than $x$. The number of these items are also given.
For example ...
0
votes
2answers
47 views
Highest Product of X Items
š§© 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 ...
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, ...
-2
votes
1answer
62 views
Greedy algorithm for problem asking for solution of size *at most* $k$
Given an integer $k$ and a complete weighted bipartite graph with sides $A,B$ in which the weight of the edge $(i,j)$ is $c_{ij} \geq 0$, we want to find a set $S$ of at most $k$ edges that maximizes $...
2
votes
1answer
38 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 $i$ ($1 \le i \le m$) ...
1
vote
0answers
30 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 ...
2
votes
1answer
31 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 &...
0
votes
0answers
27 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 ...
2
votes
1answer
187 views
How to understand the solution to Task Scheduler problem on LeetCode?
LeetCode Task Scheduler problem is the following:
Given a characters array tasks, representing the tasks a CPU needs to do, where each letter represents a different task. Tasks could be done in any ...
1
vote
1answer
43 views
Serving $k$ customers with bounded time window
A person provides a service and he/she can serve $k$ clients each minute.
Now, client number $i$ comes at the beginning of minute $a_{i}$ and waits $w_{i}$ minutes to receive the service and if they ...
0
votes
1answer
41 views
Ordering the tasks to minimize penalties
So I just started learning greedy algorithms and I have a problem that I want to solve. The statement is as follows:
In your calendar you have an $L$ list of all the tasks you need to complete today. ...
-2
votes
1answer
85 views
Correctness proof of a greedy approximation algorithm
How do I prove the correctness of this algorithm?
36
votes
2answers
34k views
How to prove greedy algorithm is correct
I have a greedy algorithm that I suspect might be correct, but I'm not sure. How do I check whether it is correct? What are the techniques to use for proving a greedy algorithm correct? Are there ...
2
votes
0answers
32 views
Maximize the minimum gap while scheduling within intervals?
Problem
There are N intervals in which a particular integer can be chosen. What is the maximum possible minimum gap between each integer if one integer is chosen for each of those intervals?
For ...
0
votes
2answers
60 views
Why this problem has such a simple solution? How would you avoid looking for more complex solutions first?
There's a problem whose solution startles me because at first sigh, I wouldn't imagine that it could be solved so easily. The problem is:
There are n tasks, each task ...
0
votes
1answer
34 views
Mathematical expression for the quantity that we are maximising in the stock buying and selling problem
Problem Statement:
Say you have an array prices for which the $i^{th}$ element is the price of a given stock on day $i$.
Design an algorithm to find the maximum profit. You may complete as many ...
0
votes
2answers
62 views
What is an algorithm for minimizing the standard deviation of m sums summed from n summands? [with attempt]
I have m bins (sums) and n summands. Each summand goes into a bin. In order to minimize the standard deviation, I have a greedy algorithm that appears to accomplish this. I am not sure of the name, ...
-1
votes
1answer
35 views
Prove following statement about Kruskal Algorithm
Let G be undirected graph, G=(V,E), and all edge weights are distinct. Consider an edge e=(u,v)āE that wasn't included in the solution obtained from applying Kruskal Algorithm to G. Prove that this ...
0
votes
0answers
49 views
Find the maximum number of valid cartesian coordinates
Given a list X containing m number of x coordinates and a list Y containing m number of y coordinates. The coordinate (x, y) is valid if and only if the difference between x and y is less than or ...
2
votes
0answers
39 views
Choosing a method for algorithmic problems - is it an art or science?
I've been doing lot of programming challenges lately (such as on leetcode.com) and often find myself in a situation when I cannot pick a method for solving a problem. I stuck with questions like - ...
0
votes
1answer
82 views
Binary string satisfying several constraints
I'm trying to solve this problem, but without success.
Problem: You're given a binary string where some of the bits are replaced by ?. You're also given several ...
0
votes
0answers
18 views
Minimizing the length a Boolean Algebra Expression in disjunctive normal form
I'm looking to minimize the length of an expression in boolean algebra that has been given in disjunctive normal form and is free from redundancy. To remove redundancy from the original expression I ...
1
vote
0answers
45 views
Algorithm for summation with lowest maximum temporary sum
I've got this problem on my last exam, which I struggle to deal with.
Let's say we have array of $N$ integers (it can be float too, but let's say integers for sake of simplicity. We need to sum those ...
8
votes
1answer
397 views
The heaviest induced subgraph problem
I am interested in such a combinatorial problem: given a graph $G=(V, E)$ and a weight functions $w_v: V \mapsto R$, and $w_e: E \mapsto R$ we are asking about such a induced subgraph $G' = (V', E')$ ...
3
votes
1answer
4k views
Maximum cut using a 1/2 approximation greedy algorithm
I have the following greedy algorithm for max cut problem:
Initialization: $A \leftarrow \{v_1\}$ , $B \leftarrow \{v_2\}$
For $v \in V ā \{v_1, v_2\}$ do:
if $d(v,A) \geq d(v,B)$ then $B \...
3
votes
1answer
138 views
Using a greedy algorithm to find a cut S which at least half of the edges cut
Let $G$ be an undirected graph.
Find a greedy algorithm that finds a cut $S$ which at least half of the edges cut.
I tried to think about something like choosing the vertex with the highest degree, ...
3
votes
2answers
229 views
Difficulty in understanding the proof of the lemma : “Matroids exhibit the optimal-substructure property”
I was going through the text "Introduction to Algorithms" by Cormen et. al. where I came across a lemma in which I could not understand a vital step in the proof. Before going into the lemma ...
0
votes
1answer
412 views
Greedy sequential/parallel task scheduling
We have N tasks that need to be scheduled for processing. Each task consists of two parts that need to executed in order. The first one is guarded by a mutex and ...
0
votes
1answer
21 views
An independent d-division
I would love to have a direction for the following exercise (the material for this exercise is greedy algorithms):
Let $G = (V,E)$ an undirected graph whose vertices $V = \{v_1,\dots,v_n\}$ appear in ...
0
votes
1answer
91 views
Negative cycle detection using Bellman-Ford and its correctness
I recently started studying algorithms on my own using Cormen and MIT algo videos in YouTube. I am going thru Bellman-Ford.
I have 2 doubts about the correctness of the algorithm:
Why are we ...
0
votes
0answers
38 views
Scheduling algorithm for overlapping jobs - single resource?
I have a single resource that will need to shared for running multiple parallel jobs. Think of the resource as a straight line numbered from 1 to 100. The jobs occupy part of the line while they are ...
0
votes
1answer
61 views
Three City Scheduling
I came across the following interview question
There are 2N people a company is planning to interview. The cost of
flying the i-th person to city A is costs[i][0], and the cost of
flying the i-...
1
vote
0answers
28 views
Remove vertices to get k-connected components
In a graph, I need to remove some vertices in order to get at least k-connected components. The no. of removed vertices should be low. Is there a heuristic that I could follow for this?
1
vote
1answer
50 views
Problem related to set partitioning
Let $A_j=\{(a^i_j,b^i_j)~:~ 0 \leq i \leq n,\text{and } a^i_j,b^i_j \in \mathbb{Z}^+\}$
Given sets $A_1,\ldots, A_{p}$ and a positive integer $k$, the problem is to check whether there exists one ...
0
votes
0answers
20 views
Set Cover: Understanding the algorithm with an example
I am trying to follow the following link:
Solution for an example
They have provided solution for an example using the greedy algorithm. I have got following questions:
(1)Why start with Z, cost is 7, ...
