# Questions tagged [online-algorithms]

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### Algorithm for finding heavy hitters in a weighted stream

The problem of finding heavy hitters in a stream is defined as follows: given a $N$ sized stream of elements, return a set $\mathcal D$, such that every item which arrived at least $N\theta$ times ...
195 views

### Convergence of online convex optimization methods

I am new to this subject so this question might seem a bit trivial Assume that in each round $t\in{{1,...T}}$ we choose $x_t\in K$ where $K$ is a compact and convex set, The common methods for ...
339 views

### Lookup complexity in augmented interval tree

If we consider the following problem: Stream of intervals, coming in one at a time, which we maintain in an augmented interval tree (Interval tree). At some point in time later, we get a point, and ...
103 views

### Minimum size counter-example in a 2-machine scheduling problem proof

I'm confused about something in the main proof in this paper (sorry that it's behind a paywall, but I assume many people on here have access to such things through their university and my posting the ...
438 views

The famous FTPL algorithm  is analyzing linear cost function. Is there any generalized proof for nonlinear functions known? Note that in the last paragraph of  it says "It would be great to ...
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### Sketches, using ideal hash functions

I've been reading about sketches for processing streaming data (the CountMin sketch, the Count sketch, the tug-of-war sketch, FM sketches, etc.). They use hash functions that are required to be 2-...
493 views

### Streaming algorithms suitable for undergrad course

I am looking for interesting streaming algorithms that would be suitable for presentation in an undergraduate algorithms course. Good choices should probably satisfy the following requirements: ...
219 views

### Automatically Adapting Forgetting Factor for Online EM

I've been reading some interesting papers recently on methods for automatically and adaptively setting the learning rate in stochastic gradient descent (SGD). In particular, "No more pesky learning ...
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### Are there published algorithms for on-line creation of AVL trees from ordered streams?

Given an ordered stream of n items (n unknown in advance), it is well-known how to construct a red-black tree from them in O(n)-time. More specifically this is possible using only O(log n) additional ...
721 views

### Languages recognized by polynomial-size DFAs

For a fixed finite alphabet $\Sigma$, a formal language $L$ over $\Sigma$ is regular if there exists a deterministic finite automaton (DFA) over $\Sigma$ which accepts exactly $L$. I am interested in ...
237 views

### Definition of fractional in theoretical CS

What is the definition of the word "fractional" in algorithms? I have encountered the word in phrases like "fractional algorithm", "fractional node routing problem". Note: English is not my native ...
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### Fast algorithm for linear context finding

I am trying to figure out a quick algorithm which solves the following problem. For the rest of this question, assume $0\in\mathbb{N}$. Denote by $\mathbb{R}^\mathbb{N}$ the set of all real ...
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### Is there an online algorithm for solving any P-complete problem?

We can think of the class $NC$ as the class of problems that can be solved in parallel, whereas a $P$-complete problem probably has no parallel solution. My question is: where do online algorithms ...
357 views

### Maintaining the product of a queue of semigroup elements

I have a queue $Q$ where elements can be popped from the left and added to the right in $O(1)$ time. The elements are members of a fixed semigroup $S$ with $O(1)$ time multiplication. Let the ...
371 views

### Capacity planning algorithm resources

Let's say I have a machine with many boxes of different sizes. I want to put packages inside those boxes. Packages arrive at different time and then stay in the box for specific period of time. I need ...
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### Is it enough for linear program constraints to be satisfied in expectation?

In the paper Randomized Primal-Dual analysis of RANKING for Online Bipartite Matching, while proving that the RANKING algorithm is $\left(1 - \frac{1}{e}\right)$-competitive, the authors show that the ...
886 views

### Online Algorithms books

Are there any recent books on Online Algorithms? I know of only two books on the subject. Online Computation and Competitive Analysis by Allan Borodin and Ran El-Yaniv: This is a classic but old book,...
215 views

### What are good set size estimation algorithms for small sets (around 10-50 elements)?

I'm trying to implement an online distinct counting algorithm, and I have thousands of small sets of 32 bit IP addresses whose sizes I want to estimate with high accuracy (1-5%). I came across quite ...
265 views

### Cheap online selection with weighted comparisons

Suppose we want to find the smallest element of a set $S$, whose elements are indexed from $1$ to $n$. We do not have access to the values of these elements, but we can compare any two elements of $S$...
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### Has this online problem been studied before ?

Consider the following online problem: For $\sigma$ and $k$ fixed, given a string of symbols from alphabet $[1..\sigma]$, given one by one, guess a set $S$ of $k$ symbols such that the next ...
833 views

### maintaining a balanced spanning tree of a growing undirected graph

I am looking for ways to maintain a relatively balanced spanning tree of a graph, as I add new nodes/edges to the graph. I have an undirected graph that starts as a single node, the "root". At each ...
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### What's the difference between online and incremental optimization?

Recently I've read some stuff about incremental optimization problems, but I can't see what's the difference between those and online optimization problems. My impression is that I can define every ...
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### Is there a constant factor approximation algorithm for 2D rectangle coloring problem?

The problem we consider here is the extension of the well-known interval coloring problem. Instead of intervals we consider rectangles having sides parallel to axes. The objective is to color the ...
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### Is there an online-algorithm to keep track of components in a changing undirected graph?

Problem I have an undirected graph (with multi-edges), which will change over time, nodes and edges may be inserted and deleted. On each modification of the graph, I have to update the connected ...