# 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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16 views

### difference between using cost vs expectation in competitive ratio

The standard definition defines the ratio as the "cost" for the worst-case input for online algorithm divided by the cost of an offline algorithm that knew the entire input sequence in ...
85 views

### 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),...
44 views

### 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 ...
1 vote
29 views

### 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....
368 views

### 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 $V[v]$...
62 views

### 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 ...
33 views

### 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 ...
1 vote
70 views

### 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 (...
29 views

### 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 ...
48 views

### 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 ...
1 vote
26 views

### 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 ...
37 views

### 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 : ...
1 vote
65 views

### 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 ...
67 views

### 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, ... 1 vote
60 views

### 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 ...
43 views

### 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://...
1 vote
113 views

### 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 ...
37 views

### 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 ...
80 views

### 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 ...
16 views

### 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 ...
61 views

### Scheduling jobs online on 3 identical machines - a lower bound of 5/3

Consider the Online Scheduling Problem with $3$ identical machines. Jobs, with arbitrary size arrive online one after another and need to be scheduled immediately on one of the $3$ machines without ...
208 views

### 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 ...
105 views

1 vote
134 views

### 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 ...
1 vote
129 views

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 ...
1 vote
59 views

### 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 ...
234 views

### 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 ...
1 vote
51 views

### 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 ...
526 views

### 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 ...
1 vote
43 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 ...
263 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 ...
1 vote
23 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 ...
1 vote
69 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 ...
20 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 $x_1^{(opt)}$...
230 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 ...
41 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 ...
51 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 ...
206 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 ...
1 vote
71 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: ...
22 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, ...
357 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 ...
1 vote
263 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 ...
54 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 ...
1 vote
42 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,...
110 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 ...
88 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 ...
118 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....
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 ...