Questions tagged [greedy-algorithms]

Questions about algorithms that make at each step the locally optimal choice.

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Improving on Monte-Carlo

Can I improve on a Monte-Carlo search for the problem, described? So I have a graph/network consisting of segments a1, a2, ..., b1, b2, ..., and c1, c2, ... For all the underlying segments there is ...
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27 views

Interval partitioning problem different approach - arrange lectures in minimum number of classrooms

The problem of scheduling lectures in minimum number of classrooms is as follows: Find minimum number of classrooms to schedule all lecture so that no two occur at the same time in the same room. The ...
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1answer
48 views

Greedy Heuristics with an Altered Subset Sum/Partition Problem

Say we have a constant-time function that accepts some integer set. The function outputs True if we can split the integers into two subsets of an equal sum. If we can't partition the integers given, ...
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1answer
67 views

Given n drinks, find optimum way to spend money if for each drink the price and the expiration date is given

Let's say we are given $n$ types of drinks, integer $m$ representing the budget we have and integer $d$ representing the cost of delivery when we order some drinks. For each of the $n$ drinks we are ...
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1answer
405 views

2 approximation algorithm for the single machine scheduling problem

We are given one machine and $n$ jobs that we want to process. For the $n$ jobs we have the following data: $r_{1}, ... , r_{n}$ are the release times $p_{1}, ... , p_{n}$ are the processing times ...
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2answers
293 views

Why is Dijkstra's Algorithm more popular compared to Grassfire algorithm?

Consider algorithms to find shortest paths in a graph. The grassfire algorithm has a complexity of O(|V|) where V is the number ...
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1answer
131 views

Task Distribution Algorithm

Different machine has different efficiency on different tasks, like: ...
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2answers
135 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 ...
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1answer
169 views

Maximize the sum of chosen numbers

I have 2 problems that derive from a simple problem. I'll explain the simple one with the solution I found and after that the modified problem. Suppose there is a game with 2 players, A and B and a ...
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17 views

Greedy algorithm for feedback vertex set / greedy algorithms vs local ratio in general

A greedy algorithm for finding a minimum feedback vertex set is to pick and remove a vertex with minimum $w(v)/\delta_H(v)$, where $H$ is the current graph, until there are no more cycles left. (...
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121 views

Minimum feedback vertex set [closed]

A greedy algorithm for finding a minimum feedback vertex set is to pick and remove a vertex with minimum $w(v)/\delta_H(v)$, where $H$ is the current graph, until there are no more cycles left. (...
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1answer
228 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 ...
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1answer
42 views

Check if possible to perform n tasks, each between moment b(i) and e(i) and taking 1 time unit

I have such a task at university: we have $n$ tasks, the $i$-th of them can be done between moment $b(i)$ and $e(i)$. If we decide to perform a task in moment $x$, we finish performing it in moment $x+...
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20 views

Design a greedy algorithm by intermingling two sequences [duplicate]

I find myself solving problems for a test and the next problem I still can't solve it. There are n ordered sequences, $S_1$ to $S_n$. It is requested to intermingling them to obtain a single sequence,...
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1answer
45 views

Minimize cost of recursive pairwise sums: how to prove the greedy solution works?

The problem is in this other question. Why does this always work? It's not clear to me how one would use induction. For $n = 3$, a quick calculation shows it works, however, I don't think it ...
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1answer
761 views

How to prove a greedy algorithm that uses the longest increasing subsequence?

Here is the thing, I am solving an problem, and I think, say, I am pretty sure that I have the correct algorithm but I haven't been able to prove it because of my lack of practice prooving greedy ...
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1answer
261 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 $G' = (V', E')$ ...
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1answer
50 views

How do I minimize the cost of some algorithm that performs some operation on a list?

I stumbled upon this problem whilst studying the complexity of a simple algorithm. I used set-theoretic notation, but all the $S_i$'s are lists (I couldn't think of a better way to write the problem ...
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2answers
45 views

largest subset of pairwise intersecting intervals [closed]

Given a set of intervals on the real line, compute the largest subset of pairwise intersecting intervals (an interval in the subset must intersect with every other interval in the subset). Design a ...
2
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1answer
65 views

Gas Station problem : Fixed path variation

Given a set of cities where you need a certain amount of fuel to travel from one city to another, each city has a different fuel price and you can only load K amount of fuel to the vehicle. The path ...
3
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1answer
103 views

Prove that the greedy algorithm to remove k digits from a n-digit positive integer is optimal

Given a positive n-digit integer, such as 1214532 (n=7), remove k digits (for example k=4) such that the resulting integer is the smallest one. A greedy algorithm for this would keep removing digits ...
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3answers
182 views

Selecting items from two arrays without duplicate indices to get maximum sum

Given two arrays both of length n, you have to choose exactly k values from the array 1 and n-k values from the other array, such that the sum of these values is maximum, with constraint that if you ...
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33 views

Take k numbers from the array and xor them with x to get maximum sum [duplicate]

Given an array A of n numbers and integers k and x. We can perform the following operation any number of times (including zero times). Take exactly k numbers from the array and replace each of them ...
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2answers
475 views

Split array into contiguous subarrays of approximately same sums

My question is similar to this splitting question, but my objective function is different. Looking for an algorithm to split array of $n$ positive (integer) numbers into $N$ contiguous non-empty ...
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1answer
33 views

Difference between greedy and work conserving scheduler for DAG

For both schedulers I have found the definition, that no processor stays idle, if there is more work it can do. However, I found two different upper bounds on the computation time of $T$. For the ...
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2answers
263 views

Why does this greedy algorithm fail to accurately determine whether a graph is a perfect matching?

I came across this problem in Tim Roughgarden's course on Coursera: In this problem you are given as input a graph $T=(V,E)$ that is a tree (that is, $T$ is undirected, connected, and acyclic). A ...
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1answer
2k views

How does the nearest insertion heuristic for TSP work?

In my theoretical computer science class and we were covering "Heuristics". In it we covered "Greedy Heuristics" for the "Vertex Cover Problem", "Interval Scheduling" and the "Traveling Salesperson ...
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2answers
59 views

Maximize number of museums visited in a day

Given a list of museums, their opening hours and time needed to visit each, make a schedule such that a tourist visits maximal number of museums in a given day. Suppose that no time is needed in ...
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1answer
116 views

Modified Knapsack Problem

I have a problem with the following optimisation problem: In total there are $n=100$ items. A quality level $L_i \in \{0,1,2,3,4,5\} $ must be selected for each of these items. The greater $L_i$ is, ...
2
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1answer
49 views

What is an approximation factor for the Greedy Motif Search algorithm?

What is approximation factor for the Greedy Motif Search algorithm? I couldn't find an answer to my question except for the fact that the algorithm has a unknown aproximation factor. I'm not a native ...
4
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2answers
224 views

Greedy Algorithms for Non-monotone Submodular Maximization with Cardinality Constraints

Does any approximation algorithm exist for maximization non-monotone submodular functions that might have negative values or be unbounded below? Fact 1: For monotone submodular functions, Nemhauser, ...
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43 views

Interval scheduling with shared resources between steps

I'm working on a (real life!) scenario that involves scheduling workers on an assembly line. Let's say it involves steps a -> b -> c -> d -> e, and each ...
2
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0answers
35 views

Heuristic for searching for solutions on an 8-puzzle variant with non-unique tiles

I'm trying to perform an A* search on a particular N-puzzle variant in which some tiles are identical. More specifically, assuming an $m \times m$ grid, there are m colors with m tiles of each. The ...
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1answer
50 views

Proof for optimal interval scheduling using a Greedy Approach

You are given a set of n jobs, where each job j is associated with a size s(how much time it takes to process the job) and a weight w(how important the job is). Suppose you have only one machine ...
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91 views

Maximum matching blossom algorithm

https://stanford.edu/~rezab/classes/cme323/S16/projects_reports/shoemaker_vare.pdf Why do we use blossom contrast in maximum matching? The examples that I have seen can easily be solved by just ...
2
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1answer
89 views

Can a greedy algorithm have more than one subproblems to solve after making greedy choice?

For example: s = <s1 s2 s3> is my problem, I make greedy choice s2 and solve s1 and <...
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2answers
2k views

Minimum difference between two subsets of an array of integers

The Problem Suppose we have an array A[1...n] of integers, with values ranging from 0 to K (so 0<=A[i]<=K for each i). We need to describe an algorithm to find an (X,Y) partition from the set {...
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2answers
70 views

Putting as many items as possible with weight and size limit

I am trying to design a greedy algorithm that has to take in multiple factors when making a greedy choice. Any item has an item weight of Iw and item size of <...
2
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1answer
136 views

Greedy algorithm for even item distribution

I have this problem where I need to design a greedy algorithm. The problem is as follows: A chocolate factory owns $n$ stores, which are connected by a single road. Each store has a limited supply $...
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0answers
27 views

Greedy Approach without constraint and a feasibility function

We know that the Greedy Approach in general, picks an element from a set of candidate elements that satisfies a predefined criteria (selection function) and is added to the solution if it satisfies ...
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1answer
109 views

Carpet into Box

Given a carpet of size a * b [length * breadth] and a box of size c * d, one has to fit the carpet in the box in the minimum number of moves. A move is to fold the carpet in half, either by length or ...
3
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1answer
113 views

Length of shortest codeword in Huffman encoding

Under Huffman Encoding, if one character occurs more than 1/3rd of the time, is it guaranteed that there will be at least one character whose codeword is of length 1? I thought of 2 cases where this ...
3
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2answers
192 views

Merging balls interview problem

Here is an interview problem about balls rolling towards buckets from Sprinklr Interview Experience at GeekforGeeks. You are given $n$ balls on the table and all the balls are rolling towards the ...
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1answer
37 views

Minimum Spanning Tree with one particular edge minimised(continued)

I have recently encountered a coding problem, specifically, the CCC problem S4. In the problem, it states that you are given a spanning tree, or otherwise a "valid plan of pipes", that connect each ...
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2answers
62 views

Minimum spanning tree such that one edge can be minimised

During a computer coding exam, I have encountered such a problem. Given a list of vertexes and edges between the vertexes,and a positive number, D, what is the minimum spanning tree between the ...
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1answer
59 views

Number Theory Problem from Local Selection Contest EPFL | ETHZ

This was a question from the 2016 local (selection) contest in ETHZ, You have a high-precision alarm clock with three operations: 1) reset wake-up time to midnight (00:00:00.000000) 2) modify the ...
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1answer
50 views

Trying to understand the question(well spaced points ?) better

Let us have a sorted array of n numbers and we would like to find a well spaced set of C of them, More specifically, we want to get a subset $ S\subset T$ with |S| = C and with $min_{i,j \in S,i\ne j}...
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1answer
439 views

Is my proof of my greedy algorithm to find subsequence correct?

Credit to KleinBerg and Taros Book Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. ...
2
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1answer
67 views

Greedy Solution for Selecting Prefix Sum

Given $n$ arrays. Each has size of $h$. Let $a_{i, j} \in \mathbb{I}$ be the $i$-th element of $j$-th array. You can select at most $k$ numbers from all arrays but if you pick $a_{i, j}$, you have to ...