All Questions

Filter by
Sorted by
Tagged with
3 votes
0 answers
137 views

On perm+1 and det+1

Given a balanced bipartite graph G and a planar graph H. We do not know the number of perfect matchings in G and we do not know the number of spanning trees in H. But assume they are at least 3 both. ...
Turbo's user avatar
  • 12.8k
0 votes
0 answers
46 views

Deamortization of basic COLA (Cache oblivious lookahead array)

I am reading the paper titled Cache Oblivious Streaming B-trees. I am trying to understand the deamortization technique used for basic COLA. The paper says that for every level k, for deamortization, ...
debasishg's user avatar
0 votes
0 answers
31 views

Natural communication problems that are hard only for number-in-hand protocols?

I am looking for tools to lower bound the deterministic, blackboard, number-in-hand communication complexity of a certain function which is roughly speaking $f : \{0,1\}^k \times \ldots \times \{0,1\}^...
Clay Thomas's user avatar
2 votes
0 answers
77 views

Is universal hashing fully black-box reducible to error correcting code?

Fully black-box reduction is defined as in Notions of reducibility between crytpographic primitives, O. Reingold et al. Error-correcting code is used in the black-box abstract way in the sense that ...
Kagura Hitoha's user avatar
6 votes
1 answer
385 views

Given real numbers $x_1,...,x_n$ , find the maximum of $ \frac{(x_j-x_i)^2}{j-i}$

Can it be done in linear or at least subquadratic time?
Scott Aaronson's user avatar
0 votes
0 answers
25 views

Understanding the transition rule for the Markov chain in the JSV algorithm for approximating the permanent

I was making my way through the paper by Jerrum, Sinclair, and Vigoda on developing a randomized polynomial time procedure (FRPAS) for approximating the permanent of a matrix $A$ with non-negative ...
user135520's user avatar
0 votes
0 answers
62 views

Why do we use Hoeffding inequality in UCB approach to drive the confidence set in multi-armed bandit problem?

In UCB algorithm, to drive the confidence set for unknown parameters we use Hoeffding inequality. I am wondering why we don't use Normal distribution instead which is much simpler to work with. Based ...
Katan katalan's user avatar
2 votes
0 answers
39 views

Space complexity of quantum algorithms for Subset sum

As far as I can find there are several quantum algorithms for the Subset sum problem with $2^{n/3}$ running time. Is there an algorithm with $2^{n/3}$ running time that uses much less space?
ivmihajlin's user avatar
4 votes
0 answers
129 views

Complexity of numerical 3-dimensional matching where the three multisets are identical

Consider the following problem: Input: one multiset $S = \{s_1, \ldots, s_n\}$ of positive integers written in unary Output: can we build $n$ triples that sum to the same value, using each element of ...
a3nm's user avatar
  • 8,916
2 votes
0 answers
36 views

Generalization of Binary Decomposition to Polynomials?

Given an integer $x\in\mathbb{Z}$, we can write its binary decomposition (and more generally base $B$ for $B\in\mathbb{Z}$, $B>1$) as $$x = \sum_{i=0} x_i B^i,$$ where $x_i \in \mathbb{Z}/B\mathbb{...
Mark's user avatar
  • 918
20 votes
10 answers
3k views

What are examples of recent relatively simple 'toolbox algorithms'?

Taking an introduction to algorithms course, one encounters quicksort, minimal spanning tree, Dijkstra, Ford–Fulkerson algorithm etc. There are also several relatively standard data structures, such ...
Per Alexandersson's user avatar
2 votes
0 answers
42 views

Effective algorithms for finite lattices of (higher-order) monotonous functions?

I am looking for references on effective algorithms on finite lattices or posets, and in particular on lattices of monotonous functions between two lattices, with higher-order structure -- monotonous ...
gasche's user avatar
  • 2,040
3 votes
2 answers
121 views

What is formal definition of non-deterministic algorithm in context of primitive/general recursion?

I want to understand general method for formally defining non-deterministic algorithm. But all formal definitions I see are related to FSM/Turing-machines. What is the reference for non-deterministic ...
uhbif19's user avatar
  • 295
1 vote
2 answers
96 views

Do realizable systems always have some non-well-founded sets?

Suppose we are standing outside a realizable system which admits CZF or a similar constructive set theory. Then consider the following: LEM is not realized (e.g. this MSE answer) The traditional ...
Corbin's user avatar
  • 271
6 votes
1 answer
342 views

Condition Number dependent algorithms for matrix operations

Using the Conjugate gradient method we can solve a linear system $Ax=b$, where $A\in\mathbb R^{n\times n}$ in time $O(n^2 \sqrt{\kappa})$, where $\kappa=\frac{\sigma_\mathrm{max}(A)}{\sigma_\mathrm{...
Thomas Ahle's user avatar
3 votes
0 answers
73 views

Are there applications of Hyperbolic Programming other than Linear Programming and Semidefinite programming?

Title. It seems the most important special cases are LPs and SDPs. Are there other interesting special cases/applications for hyperbolic programming? (Apart from being super cool math on of itself) I ...
user3508551's user avatar
  • 1,088
3 votes
1 answer
98 views

Running time analysis of problems with a variable in problem definition

I am a research scholar in the field of algorithms and complexity theory. The problem that I am currently working is the $[1,j]$-domination problem. Given a graph $G = (V, E)$, $n = |V|$, the problem ...
Balchandar Reddy's user avatar
1 vote
0 answers
107 views

Real life application of two-way DFA

I am currently studying two-way DFA and I couldn't find and research anything on its real-life applications if there are any. I am very unsure where it could be used and any ideas would be great. tyia
user69786's user avatar
0 votes
0 answers
51 views

Learning a PAC-lernable using agnostic-PAC framework

given H a family of functions which is PAC lernable such that for $\epsilon$ error and $\delta $ confidence interval it required $m(\epsilon,\delta)$ samples. I understood that if we learn H under ...
Tomer Gigi's user avatar
7 votes
1 answer
403 views

What kind of resolution is CDCL corresponding to?

For an unsatisfiable CNF instance, CDCL will return a resolution refutation. My question : what kind of resolution does it return? tree-like, regular or general?
Jxb's user avatar
  • 315
0 votes
0 answers
30 views

Decidability of Mixed-Integer Semidefinite Programs

Semidefinite programs (SDP) have an "efficient" solution, as a convex problem, by e.g. the ellipsoid method; but this comes with standard caveats as the output can be exponentially long (...
Alex Meiburg's user avatar
2 votes
1 answer
99 views

Shortest Common Supersequence of Permutations

For integers $k$ and $n$, let $P_{k,n}$ be the set of all size-$k$ sets of permutations of $[n]$. The Shortest Common Supersequence for Permutations (SCSP) problem is: given a set $S\in P_{k,n}$, ...
igel's user avatar
  • 185
-1 votes
1 answer
87 views

How is memory being used by an algorithm, to define its space complexity? [closed]

In computation we always talk about the time and space complexity of a given algorithm. The time complexity describes how long an algorithm takes in relation to the quantity of input it receives. ...
Cybernetic's user avatar
0 votes
0 answers
58 views

kd-tree optimality for orthogonal range search

It is known that a kd-tree can be constructed for $n$ points ($k$-dimensional) in $O(n \log n)$ time and searching of any axis-aligned hyperrectangle can be done in time $O(n^{1-1/k} + out)$ time ...
karmanaut's user avatar
  • 1,177
1 vote
0 answers
45 views

Compute Fourier coefficients from Single Fourier coefficient and initial vector?

I have some vector $\vec v\in\mathbb{Z}_q^n$, and would like to obtain $n$ vectors $\vec f_0,\dots, \vec f_{n-1}$ where $\vec f_i = (\mathcal{F}(\vec v)_i,0,\dots,0)$, i.e. each vector is a single ...
Mark's user avatar
  • 918
3 votes
0 answers
92 views

I am looking for a detailed list of known reductions of NP-Complete problems

I am looking for a detailed list of known reductions of NP-Complete problems. Much like Richard Karp's list of 21 NP-Complete problems has more than a dozen reductions, I am looking for a bigger ...
Andrija Sevaljevic's user avatar
1 vote
0 answers
72 views

Using a certificate in the proof of NP hardness

Say I wanted to determine that the problem of membership in some language $L \subseteq \{0, 1\}^*$ is NP-hard. Say that I have a reduction $r: \{\text{set of quantifier free formulas} \rightarrow \{0,...
Amar Shah's user avatar
2 votes
0 answers
78 views

Status of QNC vs. PSPACE

It is known that $\text{NC} \neq \text{PSPACE}$, now I am wondering if there is a similar separation for $\text{QNC}$, the class of decision problems solvable by polylogarithmic-depth quantum circuits ...
Ilk's user avatar
  • 900
7 votes
1 answer
187 views

Can you regain the Church-Rosser property in languages with continuations?

I'm aware that if you naively add continuations to a language, the Church-Rosser property no longer holds. For example, suppose we have some variant of the STLC with basic arithmetic and integer types....
idka's user avatar
  • 81
6 votes
2 answers
610 views

NP-complete problems where the inputs are prime numbers

Are there (well?) known NP-complete problems where the input(s) is(are) a(some) prime number(s), with complexity measured relative to the binary length of the input number(s)? I am thinking there are ...
EGME's user avatar
  • 161
5 votes
1 answer
154 views

Functions with polytime iterated applications

Definitions Let $f : \{0,1\}^n \rightarrow \{0,1\}^n$ be some boolean function where the length of the output always equals the length of the input. Let $f^{k} : \{0,1\}^n \times \mathbb{N} \...
Jake's user avatar
  • 1,204
1 vote
1 answer
46 views

What is known about the complexity of Network Diversion?

In the Network Diversion problem, we are given an undirected graph $G$ on $n$ vertices, with specified nodes $s$ and $t$ and specified edge $e$, and a positive integer $k$, and are tasked with ...
Naysh's user avatar
  • 576
0 votes
1 answer
56 views

complexity of the maximum rank correlation

Given two sets of vectors of dimension $p$, $x_1,\ldots,x_m$ and $y_1,\ldots,y_n$, The Maximum Rank Correlation estimator is the vector $\beta$ given by $$\arg\max_{b\in\mathbb{R}^p}\sum_{i=1}^m\sum_{...
kara890's user avatar
5 votes
1 answer
148 views

Finding $k \times k$ rectangle in a matrix with maximum sum

Given an $n \times n$ matrix $A$ with $0-1$ entries, I want to maximize $\sum\limits_{i \in I, j \in J} a_{ij}$ subject to $|I| = |J| = k.$ I expect the problem to be NP-hard, so I want a polynomial ...
Display name's user avatar
7 votes
0 answers
191 views

Relationships between Descriptive Complexity and Average Case Complexity

Descriptive complexity gives one a logic or at least a logic to express languages in a complexity class. The PH can be defined as the union of all classes that can be expressed in Second order logic. ...
user3483902's user avatar
  • 1,181
0 votes
2 answers
33 views

Combining different length epsilon-ADU hash function families

For context, an $\epsilon$-almost delta universal ($\epsilon$-ADU) hash function family $\mathcal{H} = \{h : M \to D\}$ hashes inputs from $M$ to digests in $D$ such that for any distinct $m, m' \in M$...
orlp's user avatar
  • 720
0 votes
0 answers
42 views

Speed networking algorithm

I have 40 people and 10 tables that can accommodate 4 people at a time. The task is to make sure that every person seats with every other person at the same table exactly once, that is every person ...
Helen Grey's user avatar
2 votes
0 answers
72 views

Proof systems that may be stronger than extended Frege?

The extended Frege proof system is thought to be a fairly strong proof system, with no known superpolynomial lower bounds. But I wonder, if extended Frege is proved not to be polynomially bounded one ...
Soha's user avatar
  • 177
4 votes
1 answer
85 views

Independent set queries with preprocessing

Suppose we have a sparse undirected graph $G = (V, E)$ with $|E| = O(|V|)$, and we want to process it and then answer queries of the following type: given a set $A$, is it an independent set in the ...
Command Master's user avatar
3 votes
0 answers
205 views

Is the Fueter-Polya Conjecture proven

The Fueter–Pólya conjecture states that if $\pi$ is a polynomial function and a bijection from $\mathbb{N}^2$ to $\mathbb{N}$ then $\pi$ must be the Cantor pairing function ($(x,y) \mapsto 1/2(x + y)(...
ULechine's user avatar
  • 149
0 votes
1 answer
67 views

What's the exact complexity of a DFS if we revisit nodes?

By "revisit nodes," I mean if we didn't maintain a set of nodes we have visited. So the sum I'm examining is just the number of paths from a root to a node, across all roots and nodes. We'll ...
Adam Jamil's user avatar
-1 votes
1 answer
74 views

Find Combinations of fibonacci values to approximate a target value given $F(A,B,C,D) = (A + B + C) / D$

I am able to solve this using brute force but curious if there is a better approach. Given the function $F(A,B,C,D) = (A + B + C) / D$ where each variable is in the first 7 distinct values of the ...
john doe's user avatar
0 votes
0 answers
20 views

The minimal number of messages required to solve the mutual exclusion problem in a symmetric distributed system

In the seminal paper introducing their namesake algorithm for solving the mutual exclusion problem in a distributed system, Ricart and Agrawala assert (in the first paragraph of section 4 Message ...
Evan Aad's user avatar
  • 354
-1 votes
1 answer
124 views

Locally nameless representation implementation

ORIGINAL: I am programming a functional compiler and found out about locally nameless representation (using de brujin indeces for bound variables and names for free variables). I just don't understand ...
Deonisos's user avatar
2 votes
1 answer
102 views

clique problem in graphs with bounded degree

Is the problem of finding a clique of size $d$ in a graph of maximum degree $d$ NP-complete ($d$ part of the input)?
Michael Poss's user avatar
4 votes
1 answer
103 views

Implicit characterization of sublogarithmic space

Let $SUBLOG = DSPACE(o(\log(n)) \setminus DSPACE(O(1))$ be the set of languages decidable with less than logarithmic space, but more than a constant amount of space, on a multi-tape Turing machine ...
Jake's user avatar
  • 1,204
13 votes
2 answers
665 views

What is a very simple pseudodeterministic algorithm (for educational purposes)?

Definition. A randomized algorithm for a search problem is pseudodeterministic if it produces a fixed canonical solution to the search problem with high probability. Question. The notion of a ...
user69687's user avatar
  • 133
0 votes
0 answers
35 views

Using an offline approximation algorithm within an online algorithm

When defining an online algorithm, it is common to assume that there exists an optimal offline algorithm to be used over the set of already known requests. For example, consider the IGNORE algorithm ...
George Moneftsis's user avatar
0 votes
0 answers
65 views

Construction of a PDA for the binary and decimal representation of a number

I have the solution with me for this question but I have really hard time understanding the construction. Can anyone may be break it down in a simpler way? Problem: Given $n \in \mathbb{N}^+$. ...
Hanshika's user avatar
3 votes
1 answer
174 views

Which 1-player games are EXPTIME-complete? Also, are there any known games that are EXPSPACE-complete?

I noticed a lot of 1-player games have been shown to be NP-Hard, like Pac-Man, The World's Hardest Game, Tetris, etc. For PSPACE-Complete, I noticed that Wikipedia listed these 1-player games: It is ...
edit's user avatar
  • 33

15 30 50 per page
1
3 4
5
6 7
254