# All Questions

2 views

### N input network sorting comparators

Prove that an n-input sorting network must contain at least one comparator between the ith and (i + 1)st lines for all i = 1, 2, . . . , n − 1. Can anyon help me to solve this problem ?! Thanks in ...
52 views

### Ackermann Function Time Complexity

Are there any known problems that have an Ackermann function time complexity lower bound?
26 views

### Literature for representation for boolean functions

What is the standard literary reading to understand: $1)$ polynomial(including minimal) representation of boolean functions? $2)$ polynomial(including minimal) approximation of boolean functions? ...
30 views

### Can we design our own if clause in Normal Order evaluation

I have been reading SICP and have been thinking over a thing for quite some time related to evaluation using Substitution with ...
33 views

### Best Hamiltonian Cycle Problem solver

What is the best Hamiltonian Cycle Problem (HCP) solvers available in the market? Googling so far shows that there is one created by Flinders University that can solve at most 5000 node instances. I ...
68 views

### Gap in degree of representations of candidate boolean functions

Let $x_1,x_2,\dots x_n$ be literals. Let $P(x_1,x_2,\dots,x_n)$ be one of the following Boolean function: $0)$ Equality function - $Eq_k^n(x)=1\iff x_1+\dots+x_n= k$ $1)$ Threshold function - ...
26 views

### Safety property as closed set [on hold]

In the paper "the existence of refinement mappings", the formal definition of safety property is defined as closed set which is based on the definition of closed set: $\sigma|_m$ denote the prefix of ...
19 views

### Is the bitonic sort algorithm stable?

I was wondering, is the bitonic sort algorithm stable? I searched the original paper, wikipedia and some tutorials, could not find it. It seems to me that it should be, as it is composed of merge / ...
43 views

### how to create general star from spanning tree [on hold]

i had read a paper "Approximation algorithms for the shortest total path length spanning tree problem" .I am not getting what's a star and general star.can you explain with an example ...
52 views

### Approximate Hard Problem

The Unique Game is easy to solve for exact solutions, but becomes extremely difficult for approximate solutions, with no exact solution available. It is quite against of our intuition. As it is known, ...
36 views

### Determine if subgraph is spanning tree [on hold]

I am looking for algorithm that allow me to determine whether given subgraph is spanning tree or not.
16 views

### Constructing a tree in a Fibonacci heap with a lower bound on height [on hold]

I am trying to make a tree of height Omega(n) in a Fibonacci heap of n elements. This other SE question and page 2 of this document both provide the same idea for an algorithm that would produce the ...
26 views

### NC algorithm for rank of skinny matrix

Suppose I want to find the rank of an $m \times n$ matrix $A$ over $GF(2)$, where $m \ll n$. The algorithms for rank in the literature seem to be focused on the case when $m = n$, giving a time ...
170 views

### Are there problems for which divide-and-conquer is provably useless?

When we try to construct an algorithm for a new problem, divide-and-conquer (using recursion) is one of the first approaches that we try. But in some cases, this approach seems fruitless as the ...
91 views

### Can we decide Red-blue cut problem in polynomial time?

Given a directed graph whose arcs are coloured red and blue and integers $r$ and $b$, can we decide in polynomial time whether the digraph has a cut with at most $r$ red arcs and at most $b$ blue ...
50 views

### Candidate Boolean Function with efficient rational representation compared to polynomial representation

Let $x_1,x_2,\dots x_n$ be literals. Let $P(x_1,x_2,\dots,x_n)$ be a boolean function. Let $d$ be the smallest degree of $f(x_1,x_2,\dots,x_n)\in \mathbb R[x_1,x_2,\dots,x_n]$ that represents ...
33 views

### Will subset construction always result in a DFA? [on hold]

I understand how converting an NFA to a DFA works, but I don't understand how we are GUARANTEED to get a DFA from subset (powerset) construction. For some reason, I think there is some NFA that ...
39 views

### Diameter of Cayley graphs of subgroups of $S_n$ without inverses

Babai and Seress proved that given a subgroup $G \leq S_n$ and a generating set $S$ of $G$, any permutation in $G$ can be written as a product of generators and their inverses of length ...
20 views

### Find all the Cycle Bases in a Undirected Graph

How to find all the Cycle Bases in a Undirected Graph For example, given the graph: 0 --- 1 | | \ | | \ 4 --- 3 - 2 the algorithm should return 1-2-3 ...
54 views

### Rational function for Parity function

Let $x_1,x_2,\dots x_n$ be literals. Let $P(x_1,x_2,\dots,x_n)$ be the parity function. What is the smallest degree of $f(x_1,x_2,\dots,x_n)\in \mathbb R[x_1,x_2,\dots,x_n]$ that represents ...
39 views

### Edge-based NP-hard problems for reduction

I have a problem formulation where the input is a undirected graph $G=(V,E)$, and the task is to add a set of new edges $F \subseteq V\times V \setminus E$ to $E$, but no node $v\in V$ receives more ...
29 views

### Reference request: Classical analog of quantum threshold theorem

For quantum circuits, once the gate error is below a threshold, the error probability of an entire computation can be driven exponentially small with polylog costs in time and space: ...
24 views

### Is evolution by natural selection the most efficient form of self organization?

This question crosses a number of different categories, so I didn't know where to put it. Quite simply, if any system is able to undergo self-organization with initial inputs, and left to evole a near ...
43 views

### Efficient Reduction from Min Cut to st-Min Cut

I am aware that many known algorithms for min cut problem is not by reducing the problem to $st$-min cut. But the question of efficient reduction from min cut to $st$-min cut is still interesting to ...
25 views

### What is the resolution of the apparent contradiction in the Practical Byzantine Fault Tolerance paper?

This question refers to the paper by Miguel Castro and Barbara Liskov. On Page 4, the fourth paragraph of 4.2, it says "the primary... multicasts a pre-prepare message with m piggybacked to all the ...
31 views

### How to estimate the probability of distribution of a variable in a Constraint Satisfication Problem

Consider that we have a state space of n random variables, for simplicity, the variable value can be 0 or 1. Each variable has its probability distribution when it is not constrained, also for ...
111 views

### Does ${\bf AC^0PAD} = {\bf PPAD}$?

What happens if we define ${\bf PPAD}$ such that instead of a polytime Turing-machine/polysize circuit, a logspace Turing-machine or an ${\bf AC^0}$ circuit encodes the problem? Recently giving ...
77 views

### Automata and a kind of pumping lemma on state transition function

We encountered this question as an exercise in a Büchi automata book a couple of decades ago, and back then gave a few tries thinking that it should be easy. But haven't seen a solution. My ...
35 views

### Dynamic Multithreading Analysis of Cache Oblivious Matrix Multiplication

I am reading the paper of Frigo et. al., The Cache Complexity of Multithreaded Cache Oblivious Algorithms, 2007. They present an algorithm to multiply two $n \times n$ matrices. This algorithm is a ...
110 views

### NP-hardness of minimizing sum of weighted product

Consider a total of $d$ items, $\{I_1,I_2,\cdots,I_d\}$, each having a weight $w_i$ (a positive integer), and a total of $m$ bins, $\{B_1,B_2,\cdots,B_m\}$. We would like to distribute the items into ...
31 views

### NP-hardness of n queens problem [on hold]

i have following questions 1> is this statemnt true or false: "If we could solve an NP-hard problem in polynomial time, this would prove P = NP." 2>is n queens problen np hard or just np??? 3> iam ...