Finding a boolean submatrix isomorphic to a specific fixed set of other...
Given a matrix $M$ of certain size $h\times w$, where $h\leq w$, for example $5\times 6$, are also given the following set $B$ of additional all-ones matrices, that I like to call target...
View ArticleIs this data structure a hypertree or they are just isomorphic trees?
I have a data structure described as following:- It's a collection of trees.- Each tree has the same structure.- Each tree has information of diferent nature.A example of this data structure: 4 - - - -...
View ArticleConnected but not adjacent vertex
Are there specific terms or adjectives in graph theory to name these two situations?Two vertices are non-adjacent (disjoint? I have seen that the term "disjoint" is rather used for paths with...
View ArticleGiven a row sum vector and a column sum vector, determine if they can form a...
For example, for a boolean matrix of size $3x4$, the column sum vector $C = (3, 3, 0, 0)$ and the row sum vector $R = (2, 2, 2)$ form a match because I can construct the boolean...
View ArticleAnswer by ABu for Given a row sum vector and a column sum vector, determine...
Based on the, apparently famous paper on the field, Ryser 56, and the thesis recommended by @orlp, the test to know if a row and column sum vectors forms a match, e.g., a matrix $M_{h,w}$ exists having...
View ArticlePolynomial-time algorithm to solve the maximum vertex bipartite subgraph problem
I'm trying to find an algorithm that solves the maximum vertex biclique problem. I know that that algorithm can be solved in polynomial time (in contrast with the maximum edge biclique problem, which...
View ArticleParall execution of algorithms that solves polynomically disjoint subsets...
I was thinking in the following approach for solving a problem that is believe to be a NP-hard problems today in polynomial time, assuming the following:There exists a believed-today NP-hard problem...
View ArticleFloating-point oblivious way to compute multiset numbers
I have to compute $R = \left(\!\!{n + 1\choose k}\!\!\right)$, which happens to be:$$R = \left(\!\!{n+1\choose k }\!\!\right) = \binom{n+k}{k} = \frac{(n + k)!}{n!k!} =...
View ArticleNumber of maximal cliques in graphs without common neighbourhoods
Let's consider a graph $G(n)$ of $n$ vertices such as no two vertices in $G$ have the same exact neighbors (different open neighbourhoods to be more specific; I wonder if this kind of graphs have...
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This costs minimization problem, is it solvable in polynomial time?
I have the following problem: I have $c$ conflicts, named $(c_1, \ldots, c_c)$, where each conflict $c_i$ has certain size $s_i\in\mathbb{N}_0$: the number of times conflict $c_i$ has happened. Also, I...
View ArticleA multidimensional "moving van problem": a mix of a knapsack and a...
This problem is a mix of the bin-packing and the knapsack problems. I call it "the moving van problem": there is a moving van with a limit on the weight it can transport, and a set of boxes that you...
View ArticleAnswer by ABu for Find maximal clique consisting of at least half of the...
Each time you remove a vertex $v$ with degree $<c−1$, the degree of all its neighbours will be reduced by 1, so if any neighbor $u$ gets a degree $<c−1$ after removing $v$, remove $u$ as well;...
View ArticleAnswer by ABu for Does any language need to have a bottom type?
In actual programming languages, a function is not forced to deal explicity with input is not meant to. For a function f(x) you can say something like:// x must satisfy x != 0, otherwise inv(x) results...
View ArticleAverage branching factor of an undirected graph
I'm trying to determine, given an unweighted undirected graph, the maximum number of leaves of any travelling of the graph, which means, the maximum number of leaves among all traversals of every...
View ArticleTransforming a multidimensional 0-1 knapsack problem to a maximum weighted...
Just out of theoretical curiosity, is there a way to transform a 0-1 multimensional knapsack problem to a maximum clique problem? Or maybe even easier, to a maximum weighted clique problem (the weights...
View ArticleAnswer by ABu for Algorithm for solving a mixed integer programming problem...
Since the value of each $m_i$ doesn't matter (you can assign $m_i=\lfloor a_ik\rfloor$ as far as the $[b_ik-1, a_ik]$ contains an integer), your problem can be re-formulated...
View ArticleMinimum number of bits to codify arrays with bounded sums
I have a very big set of non-empty arrays of possibly repeated numbers sorted in a weakly-decreasing order where each number belongs to the interval $[1, 55]$ and the sum of the elements of each array...
View ArticleRegarding CPU ILP: what actually consistitutes "the current instruction"?
If a CPU is able to execute multiple instructions in parallel, and fetching/decoding/scheduling instructions happen in batches, and there's multiple execution units, etc. What does the IP register...
View ArticleMemory-efficient representation of keys over a huge domain
I don't know if the title of the question is accurated or not, but I was thinking of the following problem:I have a set of numbers, let's call them identifiers. Each identifier is stored on a 64-bit...
View ArticlePerformance considerations of index maps for rearranging a vector
Imagine two vectors $V=[v_1, v_2, \ldots, v_n]$, $S=[s_1, s_2, \ldots, s_n]$ where $S$ is a rearrangement of $V$ based on some relation $\leq$. Imagine that, instead of computing $S$ using as input $V$...
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