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Questions tagged [sparse-matrices]

36 questions
13
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1 answer

Inverting a band matrix

I have a band matrix -- a sparse, square, symmetric $N \times N$ matrix whose structure looks like the following: Here, the area under the blue stripes is the non-zero elements; everything else is zero Is there an algorithm to invert this kind of…
rnels12
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1 answer

Chernoff-Hoeffding bounds for the number of nonzeros in a submatrix

Consider a $n \times n$ matrix $A$ with $k$ nonzero entries. Assume every row and every column of $A$ has at most $\sqrt{k}$ nonzeros. Permute uniformly at random the rows and the columns of $A$. Divide $A$ in $k$ submatrices of size $n/\sqrt{k}…
Matteo
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5
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2 answers

Data structure for sparse matrices for an online problem

I need to compute a large linear optimization problem very often after recieving updates to my optimization problem. That is I have a linear problem to find an x such that $x_1 * c_1 + ... + x_n * c_n$ is as small as possible under the conditions…
Beginner
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4
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SimRank on a weighted directed graph (how to calculate node similarity)

I have a weighted directed graph (it's sparse, 35,000 nodes and 19 million edges) and would like to calculate similarity scores for pairs of nodes. SimRank would be ideal for this purpose, except that it applies to unweighted graphs. It's easy to…
Remy
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4
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Low-rank matrix completion is NP-hard

In looking into the problem of low-rank matrix completion / relaxations of the general problem to derive exact solutions, many papers cite that the original formulation is NP-hard but I cannot find a proof of this fact. The problem is as…
Doc Stories
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4
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2 answers

Max flow algorithm for floating-point weights and E~=10*V

Could you, please, suggest a maximum flow algorithm for a graph with floating-point weights and the number of edges approximately equal to the number of vertices? I.e. O(V^3) algorithms take too much time, but O(E^2) algorithms are much more…
Serge Rogatch
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3
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1 answer

Need clarification about the use of Big-O to describe matrix sparsity

In one of my courses, Big-O notation was used for defining what a sparse matrix is, under the context of qualifying for suitability for a particular set of linear algebra algorithms. I looked around on the net, and only found more such uses that I…
Tyler
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3
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Finding the bandwidth of a band matrix

I am designing an algorithm that solves a linear system using the QR factorization, and the matrices I am dealing with are sparse and very large ($6000 \times 6000$). In order to improve the efficiency of the algorithm, I am trying to exploit the…
Vinícius Lopes Simões
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3
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1 answer

Mathematical operation for removing duplicate rows in a matrix

I am using the GraphBLAS C API (https://graphblas.org/) which provides an interface for performing mathematical operations on sparse matrices. Given an adjacency matrix $\mathbf{A}: \mathbb{R}^{n \times n}$, I would like to remove duplicate rows…
codeing_monkey
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When are adjacency lists better than sparse matrices?

I saw several questions discussion the benefits of adjacency lists over matrices to represent a sparse undirected graph. On the other hand, none of them discuss sparse matrix representations such as scipy's coo or csr formats. Do adjacency lists…
Geoffrey Negiar
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3
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Calculating diagonal of inverse of sparse band-like matrix

I'm trying find an optimization for an equation related to theorem 3.5.7 from "Finite Markov Chains" by Kemeny and Snell (1976). The theorem is: $$H=(N-I)N_{dg}^{-1}$$ Where $N_{dg}$ is a diagonal matrix with all 0 except for the diagonal portion of…
anjama
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2
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1 answer

GraphSlam Doubt

I am trying to implement Graph slam. I have some doubts regrading implementation. I attached a picture to clarify my doubt. [ I have a doubt in line number 2. It show omega have a scalar value 0. But at line 3 it show omega is a Matrix. Next doubt…
Encipher
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2
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Permutation on matrix to fill main diagonal with non-zero values

I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal is filled with non-zero values. My matrices represent a set of…
Demurgos
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2
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Fastest Algorithm for finding All Pairs Shortest Paths on Sparse Non-Negative Graph

As discussed here Johnson's Algorithm can be used to solve the APSP-Problem in $O(V^2\log V + VE)$ in stead of $O(V^3)$ for Floyd-Warshall. However, Johnsons Algorithm does quite a bit of work for the case that some weights are negative. Is there a…
Anton Ballmaier
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Optimize sorting matrix entries by row and column

I am writing a routine to store an $M$-by-$N$ sparse matrix in a balanced binary tree. The insertion routine calls a comparison function to determine where a new matrix entry $(i,j)$ should be inserted in the tree. I am defining the ordering of the…
vibe
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