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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What is the fastest online sorting algorithm?

Quoting Online algorithm from Wikipedia: In computer science, an online algorithm[1] is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed ...
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1answer
113 views

Can map-reduce speed up the count-min-sketch algorithm?

Is there any possibility of improvement in the result of count-min-sketch algorithm if we will use Map Reduce approach? Improvement in performance can be in terms of accuracy, time complexity or the ...
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35 views

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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19 views

Online bipartite matching problem for task assignment

I have $n$ drivers, each one has a balance (in Us dollars), availability status (true if he is not working already) and number of accomplished tasks in the current ...
2
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1answer
80 views

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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0answers
94 views

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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0answers
16 views

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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2answers
64 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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0answers
52 views

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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14 views

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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1answer
38 views

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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27 views

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 ...
2
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1answer
150 views

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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1answer
21 views

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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0answers
168 views

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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1answer
144 views

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 ...
14
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3answers
3k views

Determine missing number in data stream

We receive a stream of $n-1$ pairwise different numbers from the set $\left\{1,\dots,n\right\}$. How can I determine the missing number with an algorithm that reads the stream once and uses a memory ...
2
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1answer
102 views

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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0answers
38 views

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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0answers
37 views

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,...
3
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1answer
64 views

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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1answer
72 views

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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1answer
159 views

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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2answers
112 views

Online sorting without modifications

There is an array with $n$ places. There is a stream of $n$ unique numbers that arrive at a random order (permutation selected uniformly at random). Whenever a number arrives, we must put it ...
3
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0answers
157 views

Online bipartite edge-cover problem with requirements

I have $N$ nodes $v_1,\ldots,v_N$ in one partition $X$ and $M \leq N$ nodes $u_1,\ldots,u_M$ in a different partition $Y$. I want to connect nodes in $X$ to nodes in $Y$ with edges under the following ...
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0answers
86 views

Competitive ratio of this paging algorithm

In the paging problem, we have a cache of size $k$ and a universe of $n>k$ pages. In an online setting, we get requests for pages $p_1,p_2,\ldots p_t$, and are required to have page $p_i$ loaded ...
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1answer
343 views

Methods for proving upper bound on a-approximiation algorithms? [closed]

I'm dealing with some simple randomized and on-line algorithms, both kind produce some lower/upper bound on quality of the output instance. For example, there's a simple randomized algorithm for the ...
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1answer
63 views

Search a preprocessed text with online queries

We're given a fixed text, and we are presented with a series of online queries of patterns. For each query, the goal is to answer if the pattern exists in the text. Each pattern is a string, and we ...
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0answers
126 views

Winnow versus Perceptron - Why adding irrelevant features increases L2(X) but not L∞(X)?

I saw here: http://www.cs.cmu.edu/~ninamf/ML11/lect0906.pdf Intuitively, if “n” is large but most features are irrelevant (i.e. target is sparse but examples are dense), then Winnow is better because ...
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2answers
598 views

Online generation of uniform samples

A source provides a stream of items $x_1, x_2,\dots$ . At each step $n$ we want to save a random sample $S_n \subseteq \{ (x_i, i)|1 \le i \le n\}$ of size $k$, i.e. $S_n$ should be a uniformly chosen ...
5
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2answers
347 views

Data structure for sparse matrices for an online problem

I need to compute a large linear optimization problem very often after recieving updates to my optimization problem. That is I have a linear problem to find an x such that $x_1 * c_1 + ... + x_n * ...
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1answer
290 views

Keep k+ties largest elements in a stream

I have $n$ numbers that come one by one, and when the last element comes, I want to output $k$ largest elements and those that are ties with the minimal element from this top-$k$ element. For ...
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1answer
844 views

Online supervised learning algorithm

I have labeled examples coming in on the fly, thus I need to create a classifier from sequential data instead of a static example set. Incoming data is fully labeled, there are no unlabeled examples. ...
2
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1answer
1k views

Load balancing. Why not use priority queues?

I have recently learned about various randomized algorithms for load balancing. The model is always that there are $m$ balls and $n$ bins and the balls arrive one at a time. The task is to minimize ...
1
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1answer
81 views

Online and parallizeable set intersection algorithm

I have problem that is reducible to the following: From a collection of stacks, find all items whose "keys" are on all stacks. My current solution to this problem is to just pop things off as ...
5
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2answers
619 views

Lazily computing a random permutation of the positive integers

Are there any existing efficient algorithms for lazily computing a random permutation of the positive integers in a given range (e.g. the range offered by an unsigned integer type in a CPU)? What I ...
3
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1answer
45 views

Packing unsplittable flows problem

For a single stream of elements as input every elements should be routed into a fixed number of $k$ output streams trying to keep them balanced. In the following example $k=3$ : Let's define as flow ...
2
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0answers
43 views

Do online quantile estimation algorithms that support deletions exist?

There are several online quantile estimation algorithms, but I haven't seen any that supports deletions (i.e. unobserve elements observed in the past). Are there any such known algorithms? To ...
11
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2answers
479 views

Fair cake-cutting when players join late

The usual statement of the fair cake-cutting problem assumes that all $n$ players get their share at the same time. However, in many cases the players arrive incrementally. For example, we may divide ...
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0answers
512 views

Streaming Knapsack Problem

I want to implement efficiently "streaming Knapsack" problem in java. The problem is I have a stream input of integer data coming continuously for example -1, 2, 9, 5, 5, 11, 1 -3,... The question ...
4
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1answer
503 views

An incrementally-condensed transitive-reduction of a DAG, with efficient reachability queries

Is there an incremental directed graph data structure that has the following properties: Keeps an internal graph structure as a DAG, and the graph is accessible (notwithstanding other helper data-...
3
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0answers
587 views

Motion planning using second order Bézier curves

I'm trying to find an algorithm for a motion planning problem. I have $N$ points, $P_1$ to $P_N$, in $k$-dimensional cartesian space, defining $N-1$ segments. The problem is about constructing the ...
3
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0answers
74 views

Online algorithm for planning

Let S be a system whose state can be altered by performing actions. Each action has two possible outcomes, and each outcome brings to a specific system state. A ...
16
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1answer
251 views

Can a perceptron forget?

I would like to build an online web-based machine learning system, where users can continuously add classified samples, and have the model updated online. I would like to use a perceptron or a similar ...
1
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1answer
113 views

How to sample uniformly from a stream of elements, some of which are unsuited?

I get values $x_t$ in an online fashion and want to buy "good" ones, where "good" means that some measure $P(x_t) >T$. Consider the following simple algorithm. ...
18
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1answer
577 views

Weighted sum of last N numbers

Suppose we're receiving numbers in a stream. After each number is received, a weighted sum of the last $N$ numbers needs to be calculated, where the weights are always the same, but arbitrary. How ...
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2answers
2k views

Computing inverse matrix when an element changes

Given an $n \times n$ matrix $\mathbf{A}$. Let the inverse matrix of $\mathbf{A}$ be $\mathbf{A}^{-1}$ (that is, $\mathbf{A}\mathbf{A}^{-1} = \mathbf{I}$). Assume that one element in $\mathbf{A}$ is ...
3
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1answer
58 views

Block detection in repeated stream

I need to recover a data block from a repeated stream of data. I'm looking to see what algorithms may already exist for this as it does not feel like a novel situation. Here are the specifics: There ...