#graphs #cyclic #equivalence #comparison #no-std

no-std graph_safe_compare

Equivalence predicate that can handle cyclic, shared, and very-deep graphs

4 releases

Uses new Rust 2021

0.2.1 Jun 19, 2022
0.2.0 Mar 27, 2022
0.1.1 Jan 29, 2022
0.1.0 Jan 28, 2022

#138 in Algorithms

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graph_safe_compare

Equivalence predicate that can handle cyclic, shared, and very-deep graphs. Implements the algorithm described in the paper Efficient Nondestructive Equality Checking for Trees and Graphs. Has enhancements to support recursion without using the call-stack to support graphs with great depth and to support multi-way comparison to support giving an ordering to graphs.

Motivation

With Rust, it is common to #[derive(PartialEq)] for types so that values can be compared. However, such derived implementations cannot handle cyclic nor very-deep inputs and will cause stack overflows when given them, and will execute inefficiently when given inputs that have much shared structure.

This crate provides functions that are safe and efficient for general shapes of graphs, that can be used as PartialEq implementations.

Examples

Degenerate D.A.G. Shape

A chain where each pair of left and right edges of a My::Branch reference the same next Rc<My> node. Without shared-structure detection, it would be traversed like a perfect binary tree with 2^(depth+1)-2 recursions, but with the shared-structure detection of this crate, it is traversed with only 2*depth recursions.

use graph_safe_compare::{robust, utils::RefId, Node};
use std::rc::Rc;
use My::*;

#[derive(Eq)]
enum My {
    Leaf { val: i32 },
    Branch { left: Rc<Self>, right: Rc<Self> },
}

impl My {
    fn new_degenerate_shared_structure(depth: usize) -> Self {
        let next = Leaf { val: 1 };
        (0..depth).fold(next, |next, _| {
            let next = Rc::new(next);
            Branch { left: Rc::clone(&next), right: next }
        })
    }
}

impl PartialEq for My {
    fn eq(&self, other: &Self) -> bool { robust::equiv(self, other) }
}

impl Node for &My {
    type Cmp = bool;
    type Id = RefId<Self>;
    type Index = usize;

    fn id(&self) -> Self::Id { RefId(*self) }

    fn get_edge(&self, index: &Self::Index) -> Option<Self> {
        match (self, index) {
            (Branch { left, .. }, 0) => Some(left),
            (Branch { right, .. }, 1) => Some(right),
            _ => None,
        }
    }

    fn equiv_modulo_edges(&self, other: &Self) -> Self::Cmp {
        match (self, other) {
            (Leaf { val: v1 }, Leaf { val: v2 }) => v1 == v2,
            (Branch { .. }, Branch { .. }) => true,
            _ => false,
        }
    }
}

fn main() {
    // A depth that is fast with the `robust` variant of this crate, but that
    // would be infeasible and either take forever, due to the great degree of
    // shared structure, or cause stack overflow, due to the great depth, if
    // another variant were used.
    let depth = 1_000_000;
    let a = My::new_degenerate_shared_structure(depth);
    let b = My::new_degenerate_shared_structure(depth);
    assert!(a == b);

    // Prevent running the drop destructor, to avoid the stack overflow it would
    // cause due to the great depth.  (A real implementation would need a `Drop`
    // designed to properly avoid that.)
    std::mem::forget((a, b));
}
Cyclic Shape

A very-simple cycle. Without shared-structure detection, it would infinitely recurse and overflow the stack, but with the shared-structure detection of this crate, it does not and it completes efficiently.

The types involved are more complicated, to be able to construct cycles.

use graph_safe_compare::{cycle_safe, utils::RefId, Node};
use std::{cell::{Ref, RefCell}, rc::Rc};
use Inner::*;

#[derive(Clone)]
struct My(Rc<RefCell<Inner>>);

enum Inner {
    Leaf { val: i32 },
    Branch { left: My, right: My },
}

impl My {
    fn leaf(val: i32) -> Self { My(Rc::new(RefCell::new(Leaf { val }))) }

    fn set_branch(&self, left: My, right: My) {
        *self.0.borrow_mut() = Branch { left, right };
    }

    fn new_cyclic_structure() -> Self {
        let cyc = My::leaf(0);
        cyc.set_branch(My::leaf(1), cyc.clone());
        cyc
    }

    fn inner(&self) -> Ref<'_, Inner> { self.0.borrow() }
}

impl PartialEq for My {
    fn eq(&self, other: &Self) -> bool {
        cycle_safe::equiv(self.clone(), other.clone())
    }
}
impl Eq for My {}

impl Node for My {
    type Cmp = bool;
    type Id = RefId<Rc<RefCell<Inner>>>;
    type Index = u32;

    fn id(&self) -> Self::Id { RefId(Rc::clone(&self.0)) }

    fn get_edge(&self, index: &Self::Index) -> Option<Self> {
        match (index, &*self.inner()) {
            (0, Branch { left, .. }) => Some(left.clone()),
            (1, Branch { right, .. }) => Some(right.clone()),
            _ => None,
        }
    }

    fn equiv_modulo_edges(&self, other: &Self) -> Self::Cmp {
        match (&*self.inner(), &*other.inner()) {
            (Leaf { val: v1 }, Leaf { val: v2 }) => v1 == v2,
            (Branch { .. }, Branch { .. }) => true,
            _ => false,
        }
    }
}

fn main() {
    let a = My::new_cyclic_structure();
    let b = My::new_cyclic_structure();
    assert!(a == b);

    // (A real implementation would need to break the cycles, to allow them to
    // be dropped.)
}
Multi-way Comparison for Ordering
use graph_safe_compare::{basic, utils::RefId, Node};
use std::cmp::Ordering;

#[derive(Eq)]
struct My(Vec<i32>);

impl Ord for My {
    fn cmp(&self, other: &Self) -> Ordering { basic::equiv(self, other) }
}
impl PartialOrd for My {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}
impl PartialEq for My {
    fn eq(&self, other: &Self) -> bool { self.cmp(other).is_eq() }
}

impl Node for &My {
    type Cmp = Ordering;
    type Id = RefId<Self>;
    type Index = u8;

    fn id(&self) -> Self::Id { RefId(*self) }

    fn get_edge(&self, _: &Self::Index) -> Option<Self> { None }

    fn equiv_modulo_edges(&self, other: &Self) -> Self::Cmp {
        self.0.iter().cmp(other.0.iter())
    }
}

fn main() {
    let mut array = [My(vec![1, 2, 3]), My(vec![3]), My(vec![1, 2])];
    array.sort();
    assert!(array == [My(vec![1, 2]), My(vec![1, 2, 3]), My(vec![3])])
}

Design

  • No unsafe code.

  • No panics.

  • Very minimal dependencies.

  • Organized into modules that provide variations of the algorithm for different possible shapes of graphs. Applications with graph shapes that are limited can benefit from using a variation that only supports what is needed and avoids the overhead that other variations involve. E.g. when only shallow cyclic shapes are possible, the functions provided by the cycle_safe module are sufficient, or e.g. when only acyclic deep shapes are possible, the deep_safe module is sufficient, or e.g. when deep cyclic shapes are possible then the robust module can be used.

  • A generic module exposes the generic API (which the other modules build on) that enables customizing the parameters (both types and constants) of the algorithm to make custom variations.

  • The generic API supports fallible Results with custom error types, which can be used to achieve custom limiting, e.g. of memory-usage or execution-time.

no_std support

While the support for cyclic and deep graphs requires dynamic memory allocations internally, this can be provided without the std or alloc crates. The generic API of this crate is designed for custom provision of the needed dynamic data structures. When built without its "std" feature, this crate is no_std.

Documentation

The source-code has many doc comments, which are rendered as the API documentation.

View online at: http://docs.rs/graph_safe_compare

Or, you can generate them yourself and view locally by doing:

cargo doc --open

Tests

There are unit tests and integration tests, which can be run by doing:

cargo test --workspace

The ignored tests can be run to demonstrate the limitations of variations that do not support some shapes, and are expected to either cause stack overflow crashes or to take a very long time.

There is a package that tests using the crate as no_std, which can be run by doing:

cd test_no_std
cargo build --features graph_safe_compare/wyrng

Benchmarks

There are benchmarks of the variations, that use a node type with very little overhead, which can be run by doing:

cargo +nightly bench --profile bench-max-optim

Dependencies