Questions regarding well-defined instructions for completing a task, and relevant analysis in terms of time/memory/etc.

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0answers
20 views

Whats are the problems yet to be solved in Distributed computing?

Extension for the same question Since it was 3 years old. I would like to know the current distributed problems which needs to be solved. I tried searching in wikipedia and google. But there is no ...
-1
votes
0answers
25 views

The algorithm yields optimal ternary codes [on hold]

Steps to build Huffman Tree Input is array of unique characters along with their frequency of occurrences and output is Huffman Tree. Create a leaf node for each unique character and build a min ...
-3
votes
0answers
35 views

number of edges and weights in shortest paths?

We know the bellman-ford algorithms check all edges in each step, and for each edge if, d(v)>d(u)+w(u,v) then d(v) being updated such that w(u,v) is the weight of edge (u, v) and d(u) is the ...
3
votes
1answer
89 views

Rate of convergence for the Perron–Frobenius theorem

The Perron–Frobenius Theorem states the following. Let $A = (a_{ij})$ be an $n \times n$ irreducible, non-negative matrix ($a_{ij} \geq 0, \forall i,j: 1\leq i,j \leq n$). Then the following ...
2
votes
0answers
33 views

How to simulate sequential registers from causal ones?

Background: In distributed shared memory (DSM) model, the problem of register simulations/constructions is to simulate registers with certain characteristic out of registers with weaker features. For ...
10
votes
2answers
427 views

Fun with inverse Ackermann

The inverse Ackermann function occurs often when analyzing algorithms. A great presentation of it is here: http://www.gabrielnivasch.org/fun/inverse-ackermann. $$\alpha_1(n) = [n/2]$$ $$\alpha_2(n) = ...
-1
votes
0answers
26 views

Computational complexity for linear discriminant analysis [on hold]

The linear discriminant analysis algorithm is as follows: I want to conduct a computational complexity for it. For each step, the complexity is as follows: For each $c$, there are $N_cd$ ...
0
votes
1answer
54 views

Finding intersections of numerically implemented 1-dimensional curves on a 2-dimensional plane

Question summary: what are the known efficient algorithms to find the intersections of 1-dimensional curves living on a 2-dimensional plane? Detail: I have a set of 1-dimensional curves on a ...
8
votes
0answers
146 views

Speed-up of Boolean over Algebraic computation

I would like to know what is the maximum speed-up of algebraic computation when we work in the word RAM model. This question is motivated by this theorem from Ryan's paper: Theorem 1.2 Let $(R, ...
0
votes
0answers
67 views

Efficient generation of Tournament Graphs

How to generate all non-isomorphic tournament graphs of order $n$ in an "efficient" way ? nauty (http://cs.anu.edu.au/~bdm/nauty/) can generate non-isomorphic tournaments, what is the complexity of ...
11
votes
4answers
396 views

Additive combinatorics applications in algorithm design

I'm reading surveys by Trevisan and Lovett on applications of additive combinatoric in TCS. The majority of these applications fall under computational complexity, e.g., lower bounds. I wonder if ...
3
votes
1answer
79 views

Lower bounds for inversion counting in comparison model?

For counting the number of inversions in an array, there are many $O(n \log n)$ algorithms, e.g. the one that modifies Merge Sort. There is an easy $\Omega(n)$ lower bound simply because you have to ...
4
votes
1answer
74 views

Generalized geography on solid grid graphs

A post here For which families of graphs is Generalized Geography in $P$? mentioned that generalized geography on solid grid graphs is open. Is the question still open? A quick search on Google shows ...
16
votes
1answer
194 views

Is it enough to sort for polynomially many 0-1 sequences for a sorting network?

The 0-1 principle says that if a sorting network works for all 0-1 sequences, then it works for any set of numbers. Is there an $S\subset \{0,1\}^n$ such that if a network sorts every 0-1 sequence ...
2
votes
1answer
132 views

Efficient recalculation of the maximum flow when edge capacities are reduced

Assume that we have a (directed) graph $G(V \cup \{s, t\}, E)$ and an (integer) capacity function $c : E \mapsto \mathbb{N}$. Let $f : E \mapsto \mathbb{N}$ be a maximum $s-t$ flow on this graph. ...
7
votes
1answer
222 views

Are there any interesting open questions having to do with submodularity, specially in the intersection of theoretical machine learning?

I was interested in knowing about open research topics related with sub modularity, specially within its intersection with theoretical machine learning (and related topics). I am particularly ...
4
votes
0answers
80 views

Complexity of a naive algorithm for finding the longest Fibonacci substring

I already posted this question here but I didn't receive an answer, so I'm posting it here as well :) Given two symbols $\text{a}$ and $\text{b}$, let's define the $k$-th Fibonacci string as ...
-3
votes
1answer
95 views

Algorithm to determine if given algorithm runs in polynomial time [duplicate]

In general, the undecidability of the halting problem prohibits the general determination of an algorithm's complexity. However, I can see no reason why the halting problem prohibits one from deciding ...
4
votes
3answers
255 views

Fastest polynomial time algorithm for solving minimum cost maximum flow problems in bipartite graphs

Orlin's algorithm is known to solve minimum cost maximum flow problems in $O(|E|^2 \log |V| + |E| \; |V| \log^2 |V|)$ time, where $|E|$ and $|V|$ respectively denote the cardinalities of the edge and ...
-2
votes
1answer
109 views

Deciding CL-IS on graph efficiently

Given an arbitrary graph $G$, could there be a polynomial time algorithm to tell if it has a larger size clique $(\omega(G))$ or larger independence number$(\alpha(G))$?
7
votes
0answers
105 views

Is 4-colors precoloring extension for planar graphs fixed parameter tractable?

Given a planar graph $G=(V,E)$, there exists a quadratic algorithms for 4-coloring $G$ (and $G$ is surely 4-colorable). Assume you are given a set of $k$ constraints of the form "$v_i \text{ is ...
3
votes
1answer
129 views

Finding a minimum directed cut that splits a weakly connected bipartite graph into two such non-edgeless graphs

Consider a directed, weakly connected bipartite graph $G = (U, V, E)$ where $U$ and $V$ are sets comprising the nodes of $G$, and $E \subseteq U \times V$ is the set of edges. The task is to find a ...
3
votes
1answer
175 views

Sorted intervals query

I'm in search for a data structure which efficiently operates over closed intervals with the following properties: dynamically add or remove an interval set, and anytime change, a number ("depth") ...
6
votes
1answer
86 views

FPRAS on #P complete problems and self reducibility

I am quoting a phrase of Martin Dyer in his paper Approximate Counting by Dynamic Programming: Since 0-1 knapsack is self-reducible, existence of an fpras for the problem now follows indirectly from ...
5
votes
0answers
87 views

Applications of Combinatorial Games in Computational Biology

I'm looking for general references in the literature about applications of games algorithmics in computational biology. Q1. What are the notable cases of computational-biology or bioinformatics ...
3
votes
1answer
208 views

Two rectangles whose sum of areas is given

Given is $\mathcal{P} \in \mathbb{Z}$. Are sought two rectangles which edges have integer, positive value and sum of their areas is $\mathcal{P}$. Find this two rectangles, if you know that sum of ...
2
votes
0answers
71 views

number of iterations of this algorithm (upper bound)

Let $(A, dist)$ be a finite metric space. Consider the following "$p$-center problem": given a positive integer $p$, find a subset $B$of $A$ such that $|B| = p$ and which minimizes the number $\max_{a ...
0
votes
0answers
47 views

Proof for a subpart for the painter's problem

I've been looking at the painters problem here: http://leetcode.com/2011/04/the-painters-partition-problem-part-ii.html I'm trying to formally prove that this function, on which the algorithm is ...
5
votes
1answer
69 views

Quanitifier Free Presburger Arithmetic: Upper bound on solution size?

DISCLAIMER: I had originally posted this to CS.SE, but I've deleted it and moved it here, since it received little attention, and I think it is a research level question. According to this paper, if ...
5
votes
0answers
106 views

Implications of a deterministic polytime prime-finding algorithm

I'm wondering what are the current known uses/implications of a polynomial-time algorithm for the following problem: Given $n$ in binary, output a prime $p > n$. I'm both curious about ...
1
vote
0answers
48 views

Array partitioning with limitations on partition size

Consider an array of bytes. I want to partition the array, such that the following two conditions hold: The number of bytes within each partition (except perhaps the last one) is between L and U, ...
6
votes
1answer
146 views

Integer factorization using polynomial whose roots are prime factors

Let $n$ be a square-free positive integer, let $n=p_{1}p_{2}\ldots p_{k}$ be the prime factorization of $n$ into $k$ distinct primes $p_{i}$. For such $n$, define ...
1
vote
0answers
115 views

Consequences of the existence of the following algorithm: does it imply any complexity class separation / collapse?

Let $G$ be a $3$-regular graph. Let $O$ be the number of vertex covers of $G$ having odd cardinality, and let $E$ be the number of vertex covers of $G$ having even cardinality. Let $\Delta = O - E$. ...
2
votes
1answer
101 views

Is there a name for this Assignment definition

The standard Assignment Problem asks for an optimal one-to-one assignment between agents and tasks. Now consider the following generalization: Instead of specifying a cost of a single agent-task ...
3
votes
1answer
194 views

Graph with minimum number of edges having given sets of nodes as its paths

Consider the following problem: Input: a list of subsets $P_1, P_2, \ldots, P_k \subseteq V = \{1, \ldots, n\}$ Output: a graph $G = (V,E)$ with minimum number of edges such that for every $P_i$ ...
20
votes
1answer
307 views

Deciding emptiness of intersection of regular languages in subquadratic time

Let $L_1,L_2$ be two regular languages given by NFAs $M_1,M_2$ as input. Assume we would like to check whether $L_1\cap L_2\neq \emptyset$. This can clearly be done by a quadratic algorithm which ...
3
votes
0answers
123 views

Equivalence of deterministic finite transducers over finite/infinite words

Equivalence of deterministic finite transducers - a special case of single-valued finite transducers - is decidable because it is decidable whether a transducer is single-valued. Note that two ...
2
votes
1answer
122 views

What is the space complexity of CTL model checking?

What is the space complexity of the CTL model checking algorithm via labeling without fairness (see e.g. Model Checking by Clarke at al Section 4.1 or Principles of Model Checking by Baier et al ...
2
votes
0answers
84 views

Is the problem “Binary Sorted Min Sum” already known under an other name?

A computer scientist oriented toward applications gave me the following problem: Given a positive integer $n>0$, an increasing function function $f$ and a decreasing function $g$, both ...
5
votes
0answers
165 views

Rebalancing balanced binary search tree when decreasing all keys to the right of a path?

Given a balanced binary search tree, suppose I have an operation decrease-right-keys(k, s) that operates as follows: when I call this operation on a tree $T$, I decrease all keys by $s$ in the right ...
1
vote
0answers
106 views

Scheduling to maximize idle time

In the context of scheduling maintenance jobs on arcs of a flow network I came across the problem to schedule jobs, indexed by $j$, and given by triples $(r_j,d_j,p_j)$ of (integer) release time, due ...
0
votes
1answer
123 views

Idea for a white-box PIT deterministic algorithm in polynomial time

Just a warning, I am an amateur and this algorithm probably doesn't work. A high level description of the algorithm: Be $f(x_1,...,x_n)$ a polynomial, $n$ the number of variables and $d$ is the ...
8
votes
0answers
64 views

Finding a median in a union of sets given as sorted arrays [duplicate]

You are given $k$ sorted arrays $A_1, A_2, ..., A_k$, each containing $n$ elements. How fast can you compute the median of $A_1 \cup A_2 \cup ... \cup A_k$ ? I have a solution running in ...
-1
votes
1answer
177 views

Finding $x_1,x_2,…,x_k$ such that $n=x_1!+x_2!+…+x_k!$ and $k$ is minimal [closed]

Here is a problem I'm trying to solve: Given an integer $n$ return a list $[x_1,x_2,...,x_k]$ such that $n=x_1!+x_2!+...+x_k!$ and $k$ is as low as it can be. I'm thinking of creating a list of n ...
2
votes
1answer
109 views

Solving a system of sums-of-powers polynomials

What is the complexity of calculating the values of the integers $x_i$, where $0 \leq x_1 < x_2 < \dots < x_k < n$, given only the values $s_m = \sum_{i=1}^k x_i^m$? for $1 \leq m \leq k$? ...
0
votes
0answers
29 views

how to efficiently compute mean function m(t) for non-homogeneous Poisson

Suppose that I know all intensity functions lambda(t) during given period [0,t], how can I compute the mean function m(t) for non-homogeneous Poisson process? Basically, m(t) in the integral of ...
7
votes
0answers
171 views

Time complexity of a branching-and-bound algorithm

Theoretical computer scientists usually use branch-and-reduce algorithms to find exact solutions. The time complexity of such a branching algorithm is usually analyzed by the method of branching ...
2
votes
2answers
215 views

Counting occurences of 'a' in a book faster than O(n)? [closed]

I was asked the following question in an interview: How would you count the occurrences of character a in a 500-page book? For simplicity, assume that you are ...
6
votes
0answers
106 views

Maximum weight “fair” matching

I'm interested in a variant of the maximum weight matching in a graph, which I call "Maximum Fair Matching". Assume that the graph is full (i.e. $E=V\times V$), has even number of vertices, and that ...
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votes
0answers
36 views

FPTAS for bin packing [closed]

If an algorithm for bin packing has a guarantee of OPT(I)+log^2(OPT(I)), then there is a fully polynomial approximation scheme for this problem. I have to prove this statement, but I have no idea ...