graph.dl

/*
Copyright (c) 2021 VMware, Inc.
SPDX-License-Identifier: MIT

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*/

/* Functions and transformers for use in graph processing */

/* Compute strongly connected components of a directed graph:
 *
 * Type variables:
 * - `'E` - type that represents graph edge
 * - `'N` - type that represents graph node
 *
 * Arguments:
 * - `Edges` - relation that stores graph edges
 * - `from`  - extracts the source node of an edge
 * - `to`    - extracts the destination node of an edge
 *
 * Output:
 * - `Labels` - (node, scc_id) tuples
 *    These tuples partition a subset of graph nodes into strongly
 *    connected components represented by labeling these nodes
 *    with SCC ids.  An SCC id is id of the smallest node in the SCC.
 *    A node not covered by the partitioning belongs to an SCC
 *    with a single element (itself).
 */
extern transformer SCC(Edges:   relation['E],
                       from:    function(e: 'E): 'N,
                       to:      function(e: 'E): 'N)
    -> (SCCLabels: relation [('N, 'N)])

/* Compute connected components of a graph
 * (by propagating node IDs forward, retaining the minimum ID)
 *
 * Type variables:
 * - `'E`  - graph edge
 * - `'N`  - graph node id
 *
 * Arguments:
 * - `Edges`  - relation that stores graph edges
 * - `from`   - extracts the source node of an edge
 * - `to`     - extracts the destination node of an edge
 *
 * Output:
 * - `Labels` - (n,l) tuples with final labeling of node `n`
 *    with the smallest node id `l` such that `n` is reachable
 *    from `l`.
 */
extern transformer ConnectedComponents(Edges:   relation['E],
                                       from:    function(e: 'E): 'N,
                                       to:      function(e: 'E): 'N)
    -> (CCLabels: relation [('N, 'N)])

/* Optimized version of `ConnectedComponents` for graph with nodes of type
 * `bit<n>`, n <= 64.
 */
extern transformer ConnectedComponents64(Edges:   relation['E],
                                         from:    function(e: 'E): 'N,
                                         to:      function(e: 'E): 'N)
    -> (CCLabels: relation [('N, 'N)])

/* Compute a subset of bidirectional graph edges, i.e., all edges `(x,y)` such
 * that `(y,x)` is also an edge in the graph.
 *
 * This transformer is equivalent to the following DDlog rule, but can be more
 * memory efficient, as it only computes one arrangement of `Edges` instead of two
 * (note, however, that if your program already uses at least one of the
 * two arrangements elsewhere then this transformer will not improve on its
 * memory footprint).
 * ```
 * BiEdges(x,y) :- Edges(x,y), Edges(y,x).
 * ```
 *
 * WARNING: This transformer assumes that the `Edges` relation is distinct,
 * e.g., it is an input relation.  It will return INCORRECT result otherwise;
 * hence the `Unsafe` prefix.
 *
 * Type variables:
 * - `'E`  - graph edge
 * - `'N`  - graph node id
 *
 * Arguments:
 * - `Edges`  - relation that stores graph edges
 * - `from`   - extracts the source node of an edge
 * - `to`     - extracts the destination node of an edge
 *
 * Output:
 * - `BiEdges` - the subset of all bidirectional edges of the graph.
 *   Note: this subset will contain edges in both directions, i.e., for every
 *   `(x,y)` it also contains a `(y,x)`
 */
extern transformer UnsafeBidirectionalEdges(Edges:   relation['E],
                                            from:    function(e: 'E): 'N,
                                            to:      function(e: 'E): 'N)
    -> (BiEdges: relation [('N, 'N)])