Questions tagged [greedy-algorithms]

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

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240 views

what is the significance of the word “Sub-problems” in Greedy Method?

With respect to Dynamic Programming we make a statement that : Greedy algorithm have a local choice of the sub-problems whereas Dynamic programming would solve the all sub-problems and then ...
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1answer
106 views

Why does the given solution to this problem works? How can it's correctness be proven?

This is a question asked in Adobe interview: Given heights of n towers and a value k. We need to either increase or decrease height of every tower by k (only once) where k > 0. The task is to ...
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1answer
55 views

Group values up to a threshold and minimize groups

Given a threshold $t$ and a list of numbers $N$. $\forall n \in N: n \leq t$ Now group the numbers so that the sum of the numbers $s$ is lower or equal $t$. Minimize the amount of groups. Example: $...
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1answer
236 views

Verifying if a greedy solution is optimal for a specific instance (Set cover)

Say I have an instance of the Set Cover problem, and use the typical greedy algorithm to obtain a solution. Is there an efficient way of verifying if, for that particular instance, the given solution ...
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1answer
79 views

Why is this greedy algorithm claim true?

I'm taking a course about submodular functions and their applications towards influence maximization in a network. We've been discussing a greedy algorithm for selecting $k$ initial nodes to maximize ...
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40 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 ...
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17 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 ...
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28 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 ...
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1answer
60 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 ...
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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 ...
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32 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 ...
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46 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 ...
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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?
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23 views

How proof of Hoffman algorithm greedy property starts with optimal tree T?

In this paper Claim 1 states that x and y are smallest probability and there is optimal code tree in which this two characters are siblings at the maximum depth. In proof to that claim, author starts ...
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183 views

Greedy algorithm to divide objects into the lowest number of groups of a maximum size

I have n objects of independent size s, and need to group them so that the sum of the sizes of each group is smaller than a given maximum size, and the number of groups is the smallest possible. I ...
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47 views

Looking for an algorithm or similar mathematical problem for trading ownerships in shared property

Suppose there is $N$ property. Each property is owned by multiple person. (they have shared ownership) For example: $Person_1$ owns 22% of $Property_1$, $Person_2$ owns 35% of $Property_1$ and $...
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36 views

What do you call a greedy algorithm that solves a combinatorial problem by optimizing the best k>1 choices altogether?

Suppose you have a problem which goal is to find the permutation of some set $S$ given in input that minimizes an objective function $f$ (for example the Traveling Salesman problem). A trivial ...
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99 views

Tight analysis for the ration of $1-\frac{1}{e}$ in the unweighted maximum coverage problem

The unweighted maximum coverage problem is defined as follows: Instance: A set $E = \{e_1,...,e_n\}$ and $m$ subsets of $E$, $S = \{S_1,...,S_m\}$. Objective: find a subset $S' \subseteq S$ such ...
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47 views

Weighted Activity Selection Problem with allowing shifting starting time

I have some activities with weights, and I would like to select non overlapping activities by maximizing the total weight. This is known problem and solution exists. In my case, I am allowed to ...
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34 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
619 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 ...
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1answer
431 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 ...
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37 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 ...
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1answer
684 views

Minimum Number of Integers From a List that Add up to N (Dynamic Programming)

A problem I'm working on requires me to find the minimum # of integers from a given list that add up to $N$, or more specifically: Given a list $L$ of $K$ integers, $[a_1, a_2, ... , a_k$], where ...
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63 views

Is there any greedy solution for bitonic tour

I have found dynamic solution for Bitonic tour but I could not find any greedy approach for this problem. Is it possible to solve it in a greedy manner?
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103 views

Algorythm for creating Number-Rows

Given is a list of numbers. Now you build different permutations of that list while there must not be two permutations where the sum of the numbers from any point of the row to the end/beginning is ...
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49 views

minimal packing analysis using greedy

First, for the sake of notation, suppose a finite set A, where A is a set of real numbers. Then the function f(A) is defined as the sum of all the elements in A. Then here's the following problem. I ...
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140 views

how to prove correctness of this greedy algorithm? [duplicate]

I did exercise problem from Pittsburgh university cs department. homework. Question 8 is somewhat exciting. Q8 is solved using greedy algorithm but I have no idea how to prove. Below is Question. ...
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383 views

With restrictions, can the knapsack puzzle be solved with a greedy algorithm?

I know that with the knapsack problem in general, there is no known greedy algorithm to solve it. But, say we add the following constraints: • All items have values equal to their weights (for all $...
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202 views

Information gain vs Gini impurity, for Random Forest?

I was researching about the supervised algorithm called Random Forest, that made me begin to study about decision trees, and how to induce them from a set, in order to create several predictors. My ...
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156 views

find max k sequence - is it greedy?

The original problem statement is: Given a sequence of numbers $A[1..n]$, find $k < n$ consecutive numbers such that the sum of these $k$ numbers is maximized where $k$ is a positive ...
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196 views

convex hull for unsorted vertices solved by graham scan algorithm

can graham scan algorithm work with convex hull vertices when vertices are not sorted? I am investigating a convex hull algorithm that involves sorting. In fact, its running time is limited by ...
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1answer
856 views

Find a quarrel-free seating order with a greedy algorithm [duplicate]

I'm revising for an Algorithms exam and looking at a sample question it says : A group of n teenagers $t_1, \dots, t_n$ are to sit in a single row of n chairs watching a particulary boring comedy ...
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55 views

Conjecture about a matrix column swapping challenge problem

So here is the challenge problem statement: https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1512 Basically, given a 0/1 matrix, you ...
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3answers
5k views

Correctness proof of greedy algorithm for 0-1 knapsack problem

We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an ...
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48 views

How to maximize the number of buyers in a shop?

There is a shop which consists of N items and there are M buyers. Each buyer wants to buy a specific set of items. However, the cost of all transactions is same irrespective of the number of items ...
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842 views

Fast algorithm for finding a minimum cost path through points in the plane

Consider the following problem: There are $n$ points in the plane. Starting from one of them I want to visit each of them once (except the starting node which has to be visited twice) but in a way ...
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51 views

How to use greedy algorithm to solve this? [duplicate]

Possible Duplicate: How to use greedy algorithm to solve this? You are given $n$ integers $a_1, \ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ ...
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1answer
2k views

Greedy algorithms tutorial

Could anyone point me to simple tutorial on greedy algorithm for Minimum Spanning tree - Kruskal's and Prims' Method I am looking for a tutorial which does not include all the mathematical ...
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2answers
83 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 ...
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2answers
109 views

Greedy Heuristic for the Traveling Salesperson Problem

We're studying Heuristic in my Theoretical CS class, more specifically Greedy-Algorithms for the Traveling Salesperson Problem. The first one is the "next neighbor heuristic", where you start at any ...
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2answers
281 views

Minimizing the overall cost over groups

I am trying to solve the problem of minimizing the overall cost over several groups. The schema of the data goes something like this: ...
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1answer
168 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 ...
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1answer
50 views

Schedule each entree so that all entrees are completed in the shortest amount of time

Lets say we have plenty people to dress up entrees, but only one chef to cook them. Each entree $E_i$, takes $c_i$ time to cook and $d_i$ time to "dress up". The dressing up of entrees can occur while ...
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2answers
890 views

Will a Greedy algorithm give a correct result for minimum partition?

Will a greedy method of picking the item that causes the largest difference each time lead to the optimal result in the minimum partition problem? Let's say I have a set $\{a_1,a_2,a_3,...a_n\}$, now ...
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2answers
4k views

Dynamic Programming vs Greedy - coin change problem

This is a fairly common problem: Given coins of integer denominations $v_1 < v_2< ... < v_n$, make change for an amount A using as few coins as possible. Given an input of powers of $p$, ...
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1answer
70 views

Discrete optimisation in 5 variables

I need to solve the following optimisation problem and I can't come up with any solutions. Is there any algorithm to solve this type of problem. I tried to think of a greedy algorithm or brute force, ...
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1answer
3k views

Interval scheduling scheduling problem with minimal workers

I am writing a greedy algorithm for a variation of the interval scheduling problem that I haven't seen before. I have a set of jobs, each with start and finish time. All jobs in set must be assigned ...
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2k views

Sorted-greedy for Load Balancing Problem

In load balancing problem we have $m$ machines and $n$ jobs, each taking processing time $t_j$. Total processing time on the machine $i$ is $T_i =\sum_{j\in A(i)}{t_j}$, where $A(i)$ is the set of ...
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2answers
1k views

Algorithm for sorting with constraints

I've got 30 elements which has to be grouped/sorted into 10 ordered 3-tuple. There are several rules and constraints about grouping/sorting. For example: Element $A$ must not be in the same tuple ...

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