Questions tagged [competitive-ratio]
6 questions
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Prove: Self-organizing list that uses Move-to-Front is 2-Competitive
Preparing for my finals in my "advances algorithms" course. Usually there is a question to prove one of the theorems that was given over the course. I'm currently trying to write a full proof of the following statement:
Self-organizing list that…
vesii
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Lower bound on competitive ratio of $m$-machine scheduling
Given a sequence of positive reals $a_1, a_2, \dots, a_n$ and an integer $m$, for each $j$ assign $a_j$ to a machine $i$, $1< i < m$, so as to minimize the maximum, over $i$, of the sum of all reals assigned to machine $i$.
Theorem: There is no…
nataman
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How to define the potential function method for an online maximization problem?
From Online Computation and Competitive Analysis
By Allan Borodin, Ran El-Yaniv, to prove that an online algorithm $\text{ALG}$ is $c$-competitive for a minimization problem (i.e., there exists a constant $\alpha$ such that $\text{ALG}(I)\leq c\cdot…
zdm
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Competitive ratio of the ski rental problem
Reading about the Ski Rental Problem in Wikipedia, I got confused on the "when" is the buying of the skis occur. I could think of 2 possible ways, but each of them would have a different competitive ratio for a deterministic (and non- deterministic)…
shaqed
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Deterministic Algorithm for searching for object $d$ units down one road in a $k$ road intersection
Suppose we are at the centre of a $k$ road intersection (i.e, there are $k$ different roads radiating out from where we are standing, infinitely). Suppose along one of these roads is a treasure.
This treasure is along one of these roads at distance…
WretchedCreature
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How to find competitive ratio of any online algorithm?
I am starting to learn online algorithms but am still stuck in determining the competitive ratio. I cannot understand how to find it. All the research papers are so difficult to understand. Please share a proper source from which I can start my…
Michaylor Riya
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