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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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 ...
49 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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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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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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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 ...
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 ...
46 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 ...
66 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 ...
105 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 ...
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 ...
187 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 ...
495 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
117 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, ...
135 views

Different machine has different efficiency on different tasks, like: ...
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 ...
170 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 ...
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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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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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 <...
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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. ...
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 ...
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 ...
36 views

findining the smallest sum of squared lengths of the intervals I_{k}

Given a set S = { $x_{1}$, $x_{2}$, . . . , $x_{n}$} where $x_{i} \in Z$ . and a K and it is $Z^{+}$ . The goal is to ﬁnd k intervals $I_{1}, I_{2}, . . . , I_{k}$ so that each $x_{i}$ is in one ...
431 views

A greedy algorithm for the bottle filling problem

(There’s no need to write the algorithm, I just need help with the greedy choice). Problem: you are given bottles numbered 1 to n. Each bottle i has a capacity of Ci and currently contains Li. We ...
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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 ...
320 views

How this proof of fractional knapsack works?

I don't understand a step in my book proving the fractional knapsack problem: Let value of items $v_1\ge v_2\ge \dots\ge v_n$, and assume $X=\langle x_1, \dots,x_n\rangle$ are the solution by ...
288 views

set cover where only certain special subsets are allowed

I am trying to solve a problem which turns out to be a form of the set cover problem. I've implemented the greedy Set cover approximation algorithm for set cover, but it turns out to not be accurate ...
102 views

Greedy Algorithm Proof Min Swaps

Problem to get the min. no. of swaps required for arranging pairs togethe. There exists an array of size 2N with integers ranging from 0 to 2N-1 arranged at random. Each integer is paired with ...
33 views

directed edges in an undirected graph [duplicate]

Undirected graph is given which has M edges and N vertices we have to convert every edge from u−v to u→v or v→u such that the total outdegree of every vertex is even. For example, consider a graph ...
87 views

What is the optimal way to solve the following optimization problem

You are given a function $F$, which can take one or more positive integer operands. Let $L=\{a_1,a_2\ldots a_n\}$. We need to compute the function $F(L)$ using the least number of transformations/...
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MST Proof (Kleinburg & Tordos)

Consider the Minimum Spanning Tree Problem on an undirected graph G = (V, E), with a cost ≥ 0 on each edge, where the costs may not all be different. If the costs are not all distinct, there can in ...
345 views

Greedy algorithm to find Minimum Dominating Set in a tree

Is it possible to find minimum dominating set on a tree $G$ using a greedy algorithm?
202 views

Solving “coin exchange” for coins of power values by greedy algorithm

When solving the problem of coin exchange by greedy algorithm, why will we will always have the correct result if the coin values are $1, a, a^2, \cdots, a^n$, where $a\ge 2$ and $n\gt 0$? For ...
224 views

interval scheduling algorithm

can any one explain why the greedy algorithm solution i.e sorting according to finishing time is optimal in the interval scheduling algorithm ?? I want proof in layman's language. I was watching this ...