\n", "\n", "Examples of algorithms for fill-in minimization:\n", "\n", "- **Minimum degree ordering** - order by the degree of the vertex\n", "- **Cuthill–McKee algorithm** (and reverse Cuthill-McKee) - reorder to minimize the bandwidth (does not exploit graph representation).\n", "- **Nested dissection**: split the graph into two with minimal number of vertices on the separator (set of vertices removed after we separate the graph into two distinct connected graphs).
Complexity of the algorithm depends on the size of the graph separator. For 1D Laplacian separator contains only 1 vertex, in 2D - $\\sqrt{N}$ vertices." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Gaussian elimination for sparse matrices\n", "\n", "Given matrix $A=A^*>0$ we calculate its Cholesky decomposition $A = LL^*$.\n", "\n", "Factor $L$ can be dense even if $A$ is sparse:\n", "\n", "$$\n", "\\begin{bmatrix} * & * & * & * \\\\ * & * & & \\\\ * & & * & \\\\ * & & & * \\end{bmatrix} = \n", "\\begin{bmatrix} * & & & \\\\ * & * & & \\\\ * & * & * & \\\\ * & * & * & * \\end{bmatrix}\n", "\\begin{bmatrix} * & * & * & * \\\\ & * & * & * \\\\ & & * & * \\\\ & & & * \\end{bmatrix}\n", "$$\n", "\n", "How to make factors sparse, i.e. to minimize the **fill-in**?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Gaussian elimination and permutation\n", "\n", "We need to find a permutation of indices so that factors are sparse, i.e. we build Cholesky factorisation of $PAP^\\top$, where $P$ is a permutation matrix.\n", "\n", "For the example from the previous slide\n", "\n", "$$\n", "P \\begin{bmatrix} * & * & * & * \\\\ * & * & & \\\\ * & & * & \\\\ * & & & * \\end{bmatrix} P^\\top = \n", "\\begin{bmatrix} * & & & * \\\\ & * & & * \\\\ & & * & * \\\\ * & * & * & * \\end{bmatrix} = \n", "\\begin{bmatrix} * & & & \\\\ & * & & \\\\ & & * & \\\\ * & * & * & * \\end{bmatrix}\n", "\\begin{bmatrix} * & & & * \\\\ & * & & * \\\\ & & * & * \\\\ & & & * \\end{bmatrix}\n", "$$\n", "\n", "where\n", "\n", "$$\n", "P = \\begin{bmatrix} & & & 1 \\\\ & & 1 & \\\\ & 1 & & \\\\ 1 & & & \\end{bmatrix}\n", "$$\n", "\n", "- Arrowhead form of the matrix gives sparse factors in LU decomposition" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Original matrix\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
![](\"graph_dense.png\")
and ![](\"graph_sparse.png\")
\n",
"\n",
"* Why the second ordering is better than the first one?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Graph separator\n",
"\n",
"**Definition.** A **separator** in a graph $G$ is a set $S$ of vertices whose removal leaves at\n",
"least two connected components.\n",
"\n",
"Separator $S$ gives the following ordering for an $N$-vertex graph $G$:\n",
"- Find a separator $S$, whose removal leaves connected components\n",
"$T_1$, $T_2$, $\\ldots$, $T_k$\n",
"- Number the vertices of $S$ from $N − |S| + 1$ to $N$\n",
"- Recursively, number the vertices of each component: $T_1$ from $1$ to\n",
"$|T_1|$, $T_2$ from $|T_1| + 1$ to $|T_1| + |T_2|$, etc\n",
"- If a component is small enough, enumeration in this component is arbitrarily"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Separator and block arrowhead structure: example\n",
"\n",
"Separator for the 2D Laplacian matrix \n",
"\n",
"$$\n",
" A_{2D} = I \\otimes A_{1D} + A_{1D} \\otimes I, \\quad A_{1D} = \\mathrm{tridiag}(-1, 2, -1),\n",
"$$\n",
"\n",
"is as follows\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Once we have enumerated first indices in $\\alpha$, then in $\\beta$ and separators indices in $\\sigma$ we get the following matrix\n",
"\n",
"$$\n",
"PAP^\\top = \\begin{bmatrix} A_{\\alpha\\alpha} & & A_{\\alpha\\sigma} \\\\ & A_{\\beta\\beta} & A_{\\beta\\sigma} \\\\ A_{\\sigma\\alpha} & A_{\\sigma\\beta} & A_{\\sigma\\sigma}\\end{bmatrix}\n",
"$$\n",
"\n",
"which has arrowhrad structure.\n",
"\n",
"- Thus, the problem of finding **permutation** was reduced to the problem of finding **graph separator**!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Nested dissection\n",
"\n",
"- For blocks $A_{\\alpha\\alpha}$, $A_{\\beta\\beta}$ we continue splitting recursively.\n",
"\n",
"- When the recursion is done, we need to eliminate blocks $A_{\\sigma\\alpha}$ and $A_{\\sigma\\beta}$. \n",
"\n",
"- This makes block in the position of $A_{\\sigma\\sigma}\\in\\mathbb{R}^{n\\times n}$ dense.\n",
"\n",
"Calculation of Cholesky of this block costs $\\mathcal{O}(n^3) = \\mathcal{O}(N^{3/2})$, where $N = n^2$ is the total number of nodes.\n",
"\n",
"So, the complexity is $\\mathcal{O}(N^{3/2})$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Packages for nested dissection\n",
"\n",
"- MUltifrontal Massively Parallel sparse direct Solver ([MUMPS](http://mumps.enseeiht.fr/))\n",
"- [Pardiso](https://www.pardiso-project.org/)\n",
"- [Umfpack as part of SuiteSparse](http://faculty.cse.tamu.edu/davis/suitesparse.html)\n",
"\n",
"All of them have interfaces for C/C++, Fortran and Matlab "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Nested dissection summary\n",
"\n",
"- Enumeration: find a separator.\n",
"- Divide-and-conquer paradigm\n",
"- Recursively process two subsets of vertices after separation\n",
"- In theory, nested dissection gives optimal complexity. \n",
"- In practice, it beats others only for very large problems."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Separators in practice\n",
"\n",
"- Computing separators is not a **trivial task**.\n",
"\n",
"- Graph partitioning heuristics has been an active research area for many years, often motivated by partitioning for parallel computation.\n",
"\n",
"Existing approaches:\n",
"\n",
"- Spectral partitioning (uses eigenvectors of Laplacian matrix of graph) - more details below\n",
"- Geometric partitioning (for meshes with specified vertex coordinates) [review and analysis](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.4886&rep=rep1&type=pdf)\n",
"- Iterative-swapping ([(Kernighan-Lin, 1970)](http://xilinx.asia/_hdl/4/eda.ee.ucla.edu/EE201A-04Spring/kl.pdf), [(Fiduccia-Matheysses, 19820](https://dl.acm.org/citation.cfm?id=809204))\n",
"- Breadth-first search [(Lipton, Tarjan 1979)](http://www.cs.princeton.edu/courses/archive/fall06/cos528/handouts/sepplanar.pdf)\n",
"- Multilevel recursive bisection (heuristic, currently most practical) ([review](https://people.csail.mit.edu/jshun/6886-s18/lectures/lecture13-1.pdf) and [paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.499.4130&rep=rep1&type=pdf)). Package for such kind of partitioning is called METIS, written in C, and available [here](http://glaros.dtc.umn.edu/gkhome/views/metis)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Spectral graph partitioning\n",
"\n",
"The idea of spectral partitioning goes back to Miroslav Fiedler, who studied connectivity of graphs ([paper](https://dml.cz/bitstream/handle/10338.dmlcz/101168/CzechMathJ_23-1973-2_11.pdf)).\n",
"\n",
"We need to split the vertices into two sets.\n",
"\n",
"Consider +1/-1 labeling of vertices and **the cost**\n",
"\n",
"$$E_c(x) = \\sum_{j} \\sum_{i \\in N(j)} (x_i - x_j)^2, \\quad N(j) \\text{ denotes set of neighbours of a node } j. $$\n",
"\n",
"We need a balanced partition, thus \n",
"\n",
"$$\\sum_i x_i = 0 \\quad \\Longleftrightarrow \\quad x^\\top e = 0, \\quad e = \\begin{bmatrix}1 & \\dots & 1\\end{bmatrix}^\\top,$$\n",
"\n",
"and since we have +1/-1 labels, we have\n",
"\n",
"$$\\sum_i x^2_i = n \\quad \\Longleftrightarrow \\quad \\|x\\|_2^2 = n.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Graph Laplacian\n",
"\n",
"Cost $E_c$ can be written as (check why)\n",
"\n",
"$$E_c = (Lx, x)$$\n",
"\n",
"where $L$ is the **graph Laplacian**, which is defined as a symmetric matrix with\n",
"\n",
"$$L_{ii} = \\mbox{degree of node $i$},$$\n",
"\n",
"$$L_{ij} = -1, \\quad \\mbox{if $i \\ne j$ and there is an edge},$$\n",
"\n",
"and $0$ otherwise.\n",
"\n",
"- Rows of $L$ sum to zero, thus there is an eigenvalue $0$ and gives trivial eigenvector of all ones.\n",
"- Eigenvalues are non-negative (why?)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Partitioning as an optimization problem\n",
"\n",
"Minimization of $E_c$ with the mentioned constraints leads to a partitioning that tries to minimize number of edges in a separator, while keeping the partition balanced. \n",
"\n",
"We now relax the integer quadratic programming to the continuous quadratic programming\n",
"\n",
"$$E_c(x) = (Lx, x)\\to \\min_{\\substack{x^\\top e =0, \\\\ \\|x\\|_2^2 = n}}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Fiedler vector\n",
"- The solution to the minimization problem is given by the eigenvector (called Fiedler vector) corresponding to the second smallest eigenvalue of the graph Laplacian. Indeed,\n",
"\n",
"$$\n",
" \\min_{\\substack{x^\\top e =0, \\\\ \\|x\\|_2^2 = n}} (Lx, x) = n \\cdot \\min_{{x^\\top e =0}} \\frac{(Lx, x)}{(x, x)} = n \\cdot \\min_{{x^\\top e =0}} R(x), \\quad R(x) \\text{ is the Rayleigh quotient}\n",
"$$\n",
"\n",
"- Since $e$ is the eigenvector, corresponding to the smallest eigenvalue, on the space $x^\\top e =0$ we get the second minimal eigevalue.\n",
"\n",
"- The sign $x_i$ indicates the partitioning.\n",
"\n",
"- In computations, we need to find out, how to find this second minimal eigenvalue –– we at least know about power method, but it finds the largest. We will discuss iterative methods for eigenvalue problems later in our course.\n",
"\n",
"- This is the main goal of the iterative methods for large-scale linear problems, and can be achieved via few matrix-by-vector products."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of vertices = 34\n",
"Number of edges = 78\n"
]
},
{
"data": {
"image/png": 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\n",
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