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

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4
votes
1answer
56 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 ...
15
votes
1answer
141 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
120 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
210 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
72 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
84 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
202 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
107 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
102 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
118 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
169 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
82 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 ...
-4
votes
0answers
33 views

hardness of approximating $|V| + OCT$

I try to establish a hardness result for the (strange) objective function "|V|+OCT", where OCT is an odd cycle transversal. I can cleary get that there is no PTAS, but I would like to improve this. ...
5
votes
0answers
83 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
206 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 ...
1
vote
0answers
61 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
46 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
66 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
45 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
141 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
114 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
100 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
191 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
291 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
121 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
164 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
105 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
174 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
106 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
135 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
214 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
104 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 ...
-3
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 ...
7
votes
4answers
262 views

Finding a permutation $p$ of $x_1, x_2, \dots, x_n$ which maximises $\sum_{i=1}^{n-1}|x_{p_{i+1}}-x_{p_i}|$

Here is the algorithmic problem I'm trying to solve: Given a list of integers $x_1, x_2, \dots, x_n$ find a permutation $p_1, p_2, \dots, p_n \in [n]$ that maximises the sum ...
5
votes
1answer
99 views

What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction?

What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction? Why? Details: http://en.wikipedia.org/wiki/Powerset_construction states that the ...
0
votes
1answer
120 views

checking isomorphism between K regular graph

Problem Input is a k regular graph of n vertices and I have to check whether this is isomorphic to another given k regular graph G. This is a restricted version of graph isomorphism in the sense that ...
10
votes
0answers
98 views

Is it possible to find the median with a linear size sorting network?

Is there a sorting network that makes only $O(n)$ comparisons and finds the median? The AKS sorting network sorts with $O(\log n)$ parallel steps, but here I am only interested in the number of ...
14
votes
1answer
368 views

Computing parity of a permutation in a streaming-fashion way

I'm looking for a one-pass algorithm which computes parity of a permutation. I assume that an input permutation is given by stream $\pi[1], \pi[2], \cdots, \pi[n]$. The output should be the parity of ...
2
votes
0answers
64 views

Recent insights on algorithms for 1D bin packing

This is just a general question on recent algorithms for the 1D bin packing problem. I just want to collect some information on this issue, so I’m grateful for any information. Especially heuristics ...
1
vote
2answers
93 views

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 ...
6
votes
2answers
271 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: ...
17
votes
2answers
170 views

Minimal cumulative set sum

Consider this problem: Given a list of finite sets, find an ordering $s_1, s_2, s_3, \ldots$ that minimizes $|s_1| + |s_1 \cup s_2| + |s_1 \cup s_2 \cup s_3| + \ldots$. Are there known algorithms ...
0
votes
2answers
142 views

Logic with Linear Programming

Can first-order logic be modeled/simulated as linear programming or integer programming? What about other forms of logic (say second order)? Update: am actually not a theory person, but more on the ...
6
votes
0answers
54 views

Reconstructing labeled poset from linear extensions

Let $(P, <, \mu)$ be a labeled poset, that is, a partial order $(P, <)$ with a labeling function $\mu$ that maps the elements of $P$ to labels in an alphabet $\Sigma$. A label list (or word) is ...