Questions tagged [online-algorithms]
Questions about algorithms that receive the input piecewise and have to make decisions, that is produce output, before having seen the whole input.
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Error correcting codes for stream of unkown size
Is there any algorithms like Reed Solomon that work for a stream of unknown data? The stream is finite but size is unknown until the stream ends.
I found some information about sliding window reed-...
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Competitiveness of online algorithm
Is it possible for an online algorithm to perform better than the optimal solution for the offline version of a problem, and if so, in what circumstances?
Doesn't competitive ratio rely on the fact ...
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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 ...
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Sorted degrees and maximal degree in dynamic graphs
Consider a sequence of vertex and edge additions and removals to an initially empty (undirected, simple) graph.
Is it possible to update the ordered list of vertex degrees in constant time (and space),...
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Algorithm for half-sample mode better than O(N^2)
The half-sample mode is a mode estimator that homes in on the highest density region of a set of samples in search of the mode. It is one of the better mode estimators, though it fails for J-shaped ...
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External regret algorithms playing dominated strategies
Edit 3/14 to refer to textbook question:
I am trying to understand the concept of external regret better, and am working through the Nisan et al. (eds.) Algorithmic Game Theory book (https://www.cs....
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Fast and compact data structure for dynamic graphs
A graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ may be represented in central memory as follows:
an associative array (hash table) $V$ gives for any $v\in \mathcal{V}$ the list of its neighbors $V[v]$...
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Does this online problem have a specific name?
I came across the following family of online problems:
Given a sequence of values of length n, the maximum value and the minimum value of the sequence, our goal:
Given min and max, we want to find a ...
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Simple efficient algorithm for dynamically maintaining max of special linear functions
Given $n$ tuples $(k_i >0,a_i >0)$, is there any efficient algorithm that can dynamically track
$$
\max_{i=1,\cdots,n} \left\{k_i\left(\sum_{j=1}^n a_j\right) - a_i\right\}
$$
in response to ...
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Hardness result for online matching
Currently studying the following paper:
"Fair Allocation in Online Markets" - Gollapudi and Panigrahi 2014
In which they present Theorem 2 as a hardness result for online maxmin matchings (...
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Online cycle detection but not quite: the Featherstitch problem
Featherstitch (Frost et al., 2007) is an approach for representing data consistency requirements for disk storage. This question concerns a graph-theoretic problem (§4.1 in the paper) that its ...
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Optimal online algorithm to guess the tree
I have a tree on $n$ vertices. Your goal is to find the adjacency list for it.
$n$ is known to you from the start. You can pick a vertex and ask for the lengths of the shortests paths from it to the ...
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Applications of derivative only, zeroth-order free optimization
I understand what is derivative-free optimization, and I am thinking a similar problem where the function $f$ we are optimizing is unknown and the only information we can acquire is the derivative. In ...
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Online algorithm for compressing multiple SETS?
Algorithms like LZW and others compress data sequences.
What I'm looking is an algorithm that compress multiple Sets. if possible online algorithm.
For example :
...
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Online approximation algorithm for median?
Is there a well-known or (relatively) easily-implementable streaming algorithm for approximating the median of the last, say, $k$ elements of a stream $c_1,c_2,c_3,\dots$?
The scenario is: I have a ...
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Which of the following statement is true?
Given two statement:
A:if inputs of a problem is online, then there is faster or equal
algorithm in view of time complexity for that problem when input is
offline.
B:if inputs of a problem is offline, ...
user132812
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Experts problem with one perfect expert
This question concerns a variant of the 'experts' problem and the randomized weighted majority algorithm that can be used to solve it.
This is the description of the problem from Wikipedia:
Imagine ...
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How to simulate online matching algorithms (implementation)
I was reading about online algorithms and bipartite matching.
I found an implementation that works fine on several websites (like geeksforgeeks).
For the online version, I found this paper
https://...
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How to prove that knapsack has no competitive algorithm
In online knapsack problem, items arrive one by one. Each time an item $i$ arrives, its weight $w_i$ is revealed. We would like to maximize, in an online fashion, the number of items placed in a bin ...
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Is there an online preprocessing algorithm for Range Minimum Queries (RMQ)?
Is there a linear time online version of the preprocessing RMQ algorithm? That is, an algorithm that allows to update the data structure when appending additional elements at the end of the input ...
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What is an optimal online algorithm and how to design it to solve NP-hard problems?
To solve an NP-hard optimization problem optimally, we can use mathematical programming or brute force techniques. I would like to know if it is possible to solve the problem in an online fashion ...
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Does regret change when the loss function is dependent on the previous predictions?
The loss function of each expert in the expert advice problem(or any online learning problem) depends on the time($t$) and expert advice at that time($f_{t}(i)$).
suppose in this problem, loss ...
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Weighted Online Matching - randomized algorithms
Let's consider the edge weighted online matching problem.
The Vertices arrive online and reveal all their current edges and edge-weights $w_e>0$. The goal is to maximize the matchings weight. An ...
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Online shortest path in ordered DAG
Suppose I have an edge-weighted connected rooted DAG $G = (V, E, r \in V, w \in E \to \mathbb{Z})$ where there exists a sequence of nonempty sets (called "levels") $L_0 = \{r\}, L_1 \subset ...
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Integrality gap in Online Problems and adaptation to competitive ratio
As we all know, in offline problems it is common practice to calculate the integrality gap to get some bound on the approximation ratio of the integral solution.
Now this gap ($IG:=\frac{OPT_{frac}}{...
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Solve the online unweighted 0-1 knapsack problem efficiently
I have $n$ items and a bin of size $B$ units. Each item $j$ consumes $w_j$ units of $B$ when placed into the knapsack. The item appears one-by-one in an online fashion. Once item $i$ appears, we must ...
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Definitions of and difference between adaptive online adversary and adaptive offline adversary?
I recently started learning about randomized online algorithms, and the Wikipedia definitions for the three adversary models are very unhelpful to put it mildly. From poking around I think I have a ...
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Proof of Fundamental Lower Bound on Regret
Online Convex Optimization sees optimization as a continuous process in which the algorithm learns new aspects of the problem and improves upon.
Every iteration consists of the player making a ...
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Matrix element value counting in O(1) space
The question arise from my customer's real-time system (RAM model, off-course), which has very limited resources.
Given an NxM matrix of integer values, we need to verify that the number of non-zero ...
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Matching Upper Bound for Online Problems
I have an online problem and I want to prove that no deterministic online algorithm is competitive.
Let $\texttt{ON}$ be an online algorithm and $\texttt{OPT}$ an optimal offline algorithm (an ...
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Finding the hidden treasure
Let's assume I am trying to find a hidden treasure.
The treasure is hidden at an uknown position x. We know that the position x of the treasure is somewhere on the integer axis (in other words x is ...
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Online Many-to-one Matching
Offline Problem
I have a graph $\mathcal{G} = (\mathcal{D} \cup \mathcal{A},
\mathcal{E})$. Each edge $e \in \mathcal{E}$ between the two vertex
sets $\mathcal{D}$ and $\mathcal{A}$ has an ...
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Approximation algorithm for weighted set cover, using multiplicative weights
It is known that the problem of fractional set cover
can be rephrased as a linear programming problem and be approximated using the multiplicative weights method, for instance this lecture note shows ...
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On the limitation of the "adversary" in randomization for online learning
While reading on randomization for online learning from the text "Online Learning and Online Convex Optimization" by Shai Shalev-Shwartz, I found the following statement (Pg 115)-
"The adversary can ...
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Multi Arm Bandit (MAB) -- Increasing reward function
In the general stochastic MAB model, the reward obtained at each trial is generally assumed to be independent of previous trials and obtained from some fixed (but unknown) distribution.
However, if ...
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Optimizing convex function in an online manner
I have a convex function of $n$ variables, $f(x_1,x_2,\dots,x_n)$ and need to find its minimizer. Are there algorithms that can retrieve the minimizer in an online fashion? i.e. solve for $x_1^{(opt)}$...
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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 ...
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Online set cover variant? Routing of requests
We have a set of $k$ path requests from $src$ to $dst$ that arrive sequentially.
Each request may have multiple paths, but can choose only one of them. For example, in the Figure shown, there are ...
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Hardness of approximation for online algorithms
Similar to the theory of hardness of approximation for (offline) approximation algorithms, has there been any work done on proving hardness guarantees for online algorithms? Theoretical lower bounds ...
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Lower bounds on regret
In "regret" styled analysis over $T$ steps of an iterative algorithm $\{x_i \in F \}_{i=1}^T$ (where $F$ is some feasible set) being given the sequence of loss functions $\{ f_i\}_{i=1}^T$ one defines ...
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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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Online Set Filling
Suppose we have 3 sets $A, B, C$ which can can hold a maximum of two elements, each. So the total number of elements that the sets can hold together i.e. total capacity (TC) is $ 3*2 = 6$.
Now, ...
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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 ...
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Is there an online algorithm for radix conversion?
Suppose I have $P$, which is the base-$p$ representation of an integer $n$ and I want to calculate it base-$q$ representation $Q$. The obvious algorithm is: interpret $P$ to obtain $n$, then ...
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What's the reason for sqrt(n) bounds in online learning?
I have a question regarding no-regret algorithms (of online learning). As far as I can see, such algorithms allow the absolute regret up to round $n$, which is $R_n$, to grow by $\sqrt{n}$. So, in the ...
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Update model parameter with new data, discarding old data
I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,...
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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 ...
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What is the best known data structure for online dk-NNG?
I want to build the distance constrained k-Nearest Neighbours Graph, i.e. for every point $p$ in the data cloud $P$ there are at most $k$ undirected edges to points that are closest among all possible ...
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Online algorithms and changing past decisions
We know that for some online problems, algorithms can decrease their competitive ratio greatly if they are allowed to change some of their past decisions (see http://epubs.siam.org/doi/pdf/10.1137/1....
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Term for open-ended algorithms
There are some enumeration problems which have little input, except for some termination criterion. Examples for the question at hand would be
enumeration of prime numbers in ascending order
...
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