Questions tagged [greedy-algorithms]

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

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66 views

Minimum square side length to enclose n circles of radius r

I thought of a problem but have no idea how to solve it. The problem is as follows: Given 2 numbers, n and r, find the side length (S) of the smallest square that encloses n circles each of radius r ...
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1answer
1k views

proof of correctness for greedy knapsack algorithm

I don't really understand why is statement 1 ≥ statement 2 in the attached picture. From what I understand the negative term in statement 2 must be greater than or equal the negative term in statement ...
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1answer
567 views

Does an algorithm exist for scheduling jobs on two processors?

I have two processors, and I want to schedule as many jobs as I can. I have their starting time and finishing time, and each job has to be unique to a processor (no overlap). I looked around and found ...
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1answer
60 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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1answer
31 views

Interval Scheduling Confusion

I am reading some notes about interval scheduling. I gives the following diagram: and states that: r2 is compatible with r3, while r2 and r1 are conflicting. Similarly, the set {r1, r3, r4} is ...
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123 views

Efficient traffic allocation

Users can be assigned to one experiment on my site. I have an API that developers use to trigger logic for each experiment. They call ExperimentEngine.run() to trigger the code logic for the ...
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41 views

Algorithm to check if exists a valid streaming sequence in O(n)?

Given n packets, each packet has b(i) bits and takes t(i) seconds to stream. We cannot send 2 packets at the same time. Given r > 0 and for each t > 0, the total number of bits we send from second 0 ...
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62 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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1answer
176 views

Activity Selection and Matroid Theory

Many people on different articles suggests that if an optimization problem has a greedy solution, the underlying structure must have matroid property. I was trying to understand this. So far, I was ...
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1answer
5k 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
107 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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1answer
755 views

Find the minimum set of intervals for given set of numbers

For any given set of real numbers, find the minimum set of intervals with length 1 that include all elements. For example, for the set: $${\{1.5,2.3,2.4,2.5,2.8,3.3,3.6,3.8}\}$$ the answer is $${\{[1....
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1answer
71 views

What do we call a greedy algorithm that tracks the best $n > 1$ solutions?

A naive greedy algorithm tries to find an optimal solution based on the best solution so far, hence it may get stuck in local optima. To avoid this problem, we may keep track of the best $n > 1$ ...
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2answers
68 views

Online set filling with redistributions

Edited: Suppose we have 4 sets $A, B, C, D $ which can can hold a maximum of two elements, each. Now, elements ($E_i$) arrive serially with properties such as: ...
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102 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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1answer
97 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
155 views

Algorithm for finding the binary sequence with no 3 consecutive ones and with highest point?

The problem is, we are given points $p_1,\ldots,p_n$ on positions of a length-$n$ binary sequence $x_1,\ldots, x_n$, and if the $i_{th}$ position of a sequence is $1$, then we "earn" $p_i$ points. So ...
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92 views

Table of incompatible turns in an intersection (steps to writing a program)

I just began reading Data Structures and Algorithms (Aho, Hopcraft, and Ullman). At the beginning, there is an example that discusses designing a traffic light for a complicated intersection of roads. ...
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2answers
767 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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1answer
118 views

Can LP for matroid polytopes be solved using the greedy algorithm?

For general linear programming (LP), i.e. optimization of a linear objective over a general polyhedron, to the best of my knowledge/recollection one can use the simplex algorithm (or hypothetically, ...
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534 views

greedy algorithms - minimizing total payment

The question: I want to buy $n$ books. In the book store there's a big sale according to which, if you buy three books, then the cheapest book in any triplet costs only 20% of its full price. Let $...
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1answer
50 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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3answers
1k views

Stable matching problem is greedy or Dynamic?

Is the stable matching problem greedy or Dynamic ? Please anyone can give a strong explanation as i tried to find it on the net but it isn't available.
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2answers
167 views

Element wise product sum of two arrays

I have two arrays, namely $a$ and $b$. Both have the same length $n$. I have to find the maximum value of $\sum a_i b_j$, in which every element can be used at most one time. My algorithm for solving ...
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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 $G' = (V', E')$ ...
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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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511 views

Solving a Rod Cutting Problem

I'm trying to come up with an algorithm for optimizing cutting a rod. Most of the examples I see online are for a stock of rod of a single length and optimizing the way to cut it up for max price. I ...
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131 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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1answer
168 views

Greedy algorithm: Minimizing the maximum of a list

Given a list $L$ of positive integers, assuming you can only modify the list by "splitting" its numbers a finite number $n$ of times. Write an algorithm which minimize the maximum of the last ...
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2answers
76 views

Optimal Partition of Book Chapters

Suppose you want to read a book with $n$ chapters, and chapter $i$ has $a_i$ pages. Now you want to read the entire book in $d$ days. But there are two restrictions: by the end of each day, you ...
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1answer
750 views

Optimizing greedy solution for choice game

Consider the following game: Two players choose numbers from a sequence of integers with even number of elements. The two can only choose from either the front or the end of the sequence. The purpose ...
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588 views

Proving a greedy algorithm

Hey so I'm studying for a midterm and I've run into this problem in the material. I'm not sure how to go about solving it. If I use regular induction in part a, I get something a bit tautological. Any ...
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370 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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1answer
221 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
764 views

Troubles understanding this Interval Scheduling question

Can someone explain how to prove what this question is asking? I'm terrible at proofs and the fact that I don't even understand the hint is very troubling. This is a homework question. Consider the ...
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1answer
2k views

Greedy algorithms: Minimum sum number pairing

Given $n$ real numbers (where $n$ is even) find a pairing which minimizes the maximum sum of a pair. I think the optimal pairing is obtained by sorting the original set, pairing the first element ...
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90 views

Generating a Covering Array Matrix with Simulated Annealing

I've been reading the following paper to understand how I can develop a non deterministic algorithm for test cases generation https://www.researchgate.net/publication/293043297_A_two-...
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1answer
235 views

A general algorithm for greedy algorithms

I have been refreshing on greedy algorithms as an algorithm design technique. I have read many sources for an explanation of what a greedy algorithm is, because I would like to put together a general ...
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1answer
61 views

Identifying set of longest time periods excluding overlapping time ranages

Suppose I have set of time records as follows 08:00 - 12:00 10:00 - 12:00 08:00 - 13:00 13:00 - 19:00 12:00 - 17:00 Now I want to select set of time records that ...
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What algorithm does OLA and UBER use for allotting taxis

More specifically : lets say i have 5 taxis , each available for booking at t=0; i have two days (48 hrs) with me how can I maximise their booking . I may not be able to clarify the question , this ...
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1answer
101 views

Globally-optimized nearest neighbors lookup

I have a set $\mathcal{A}$ of $\mathcal{m}$ vectors in $\mathbb{R}^a$. I also have a different set $\mathcal{B}$ of $\mathcal{n}$ vectors in $\mathbb{R}^a$. These two sets are disjoint: $\mathcal{A}\...
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1answer
87 views

Maximum sum difference between two sorted array elements under one condition [closed]

We're given two arrays $A$ and $B$ with size $N$ and $M$ respectively. We want to find a set $P = \{(a_1, b_1), \dots, (a_s,b_s)\}$ such that for each $i\in\{1, \dots, s\}$, $a_i\in A$, $b_i\in B$ ...
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1answer
49 views

Algorithm for finding a matrix which satisfies certain constraints [closed]

Given a list of entries entryList, determine a 4x4 matrix of which you sum up the entries specified in entryList such that there ...
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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 $v \in V − \{v_1, v_2\}$ do: if $d(v,A) \geq d(v,B)$ then $B \...
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1answer
278 views

Is there a polynomial time algorithm to determine whether an 'up down' language is 'emptible'?

Definitions: An up down language is a language whose alphabet is a set of pairs, but not characters, of two characters, where the one character in the pair is the opposite of the other character in ...
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1answer
639 views

Vertex Cover special cases

This was from a test from my university: Consider $T = t_1, t_2, \cdots, t_n$ a set of intervals of the form $(s, e)$, representing the start and end time, respectively. Now, select the minimum ...
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152 views

When does greediness guarantee optimality?

I was wondering if there is any theoretical results characterizing under what condition does greedy algorithm actually finds the optimal solution. Here is a motivating example. Suppose you are trying ...
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1answer
4k views

Is there a greedy algorithm to solve the assignment problem?

The assignment problem is defined as: There are n people who need to be assigned to n jobs, one person per job. The cost that would accrue if the ith person is assigned to the jth job is a known ...
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1answer
5k views

Difference between fractional knapsack & greedy solution

I am trying to understand what the difference is between the fractional knapsack problem using dynamic programming, and the greedy solution version. Im looking at an example of the fractional problem ...
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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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