# Computer Science newsletter

## Top new questions this week:

### "For small values of n, O(n) can be treated as if it's O(1)"

I've heard several times that for sufficiently small values of n, O(n) can be thought about/treated as if it's O(1). Example: The motivation for doing so is based on the incorrect idea that O(1) ...

asymptotics

### Why do we believe that PSPACE ≠ EXPTIME?

I'm having trouble intuitively understanding why PSPACE is generally believed to be different from EXPTIME. If PSPACE is the set of problems solvable in space polynomial in the input size $f(n)$, ...

complexity-theory complexity-classes intuition

### Determining the minimum number of edges to add in order to be 3-connected

A graph $G$ is said to be $3$-connected if it has no $2$-vertex cutsets (i.e., at least three vertices must be deleted to disconnect the graph). As far as I know, it is possible to determine if a ...

algorithms graph-theory reference-request

### What is it called when two problems are similar?

Suppose that there are two problems $P$ and $Q$. How can I say that "solving $P$ is same thing with solving $Q$"? For instance, if $P$ is NP-Hard, then we can say "$P$ can be solved in polynomial ...

complexity-theory terminology

### Is $NP$ "minimal", i.e. does $\Pi\notin NP$ imply $\Pi$ is $NP$-hard?

Suppose $\Pi$ is a decidable decision problem. Does $\Pi\not \in NP$ imply $\Pi$ is $NP$-Hard? Edit: if we assume there exists $\Pi\in coNP\setminus NP$ then we are done. Can we refute the claim ...

complexity-theory np-hard complexity-classes np

### Find set of points with maximum distance inside given intervals?

Let $A$ be a set of $n$ closed intervals, $I_i$, with both extremes positive integers. Is there an efficient algorithm to find a set of $n$ points $P_i$, with $P_i \in I_i$, such that the minimum ...

algorithms optimization intervals

### How to choose the maximum number of nodes (with constraints) from a graph

Consider a connected undirected acyclic graph $G$ with $n$ nodes and $n-1$ edges. The nodes have non-negative integer weights less than $n$. A positive integer $x$ is given and you want to choose at ...

algorithms graphs optimization trees

## Greatest hits from previous weeks:

### Applying Expectation Maximization to coin toss examples

I've been self-studying the Expectation Maximization lately, and grabbed myself some simple examples in the process: From here: There are three coins $c_0$, $c_1$ and $c_2$ with $p_0$, $p_1$ and ...

probability-theory statistics

### Does an Operating System inject its own machine code when you open a program?

I'm studying CPU's and I know how it reads a program from the memory and execute its instructions. I also understand that an OS separates programs in processes, and then alternate between each one so ...

operating-systems

## Can you answer these?

### Proof of Randomized Self-Adjusting Binary Search Tree

I developed a randomized self-adjusting binary search tree years ago, which I called a shuffle tree, but was unable to ever have it published because my proofs were rejected (with little explanation). ...

data-structures randomized-algorithms correctness-proof
 asked by Mayur Patel 1 vote

### What type of operations are seen the most at the physical disk level — reads or writes? Why?

This question came up in my operating systems class in a section about file system cache and RAID. I'm speculating that the answer is that writes are seen more at the physical disk level because an ...

operating-systems
I've encountered a system where I need to construct a sort of quasi block code: We want to communicate a symbol $s$ from a finite-sized alphabet $\mathcal{S}$ using $N$ segments of information. ...