Add two state dijkstra for wsp implementation
Summary: Added a new markdown file for concepts and a new test to test the edge case with upper bound. Reviewers: teon.banek, mtomic, dgleich, buda, ipaljak Reviewed By: teon.banek, dgleich Subscribers: pullbot Differential Revision: https://phabricator.memgraph.io/D1366
This commit is contained in:
Matija Santl
parent
7af80ebb8d
commit
5c7d3a908f
@ -12,6 +12,7 @@ data structures, multi-version concurrency control and asynchronous IO.
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* [About Memgraph](#about-memgraph)
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* [Quick Start](quick-start.md)
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* [Concepts](concepts.md)
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* [Examples](examples.md)
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* [Drivers](drivers.md)
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* [Data Storage](storage.md)
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68
docs/user_technical/concepts.md
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68
docs/user_technical/concepts.md
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@ -0,0 +1,68 @@
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## Concepts
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### Weighted Shortest Path
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Weighted shortest path problem is the problem of finding a path between two
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nodes in a graph such that the sum of the weights of edges connecting nodes on
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the path is minimized.
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More about the *weighted shortest path* problem can be found
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[here](https://en.wikipedia.org/wiki/Shortest_path_problem).
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## Implementation
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Our implementation of the *weighted shortest path* algorithm uses a modified
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version of Dijkstra's algorithm that can handle length restriction. The length
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restriction parameter is optional, and when it's not set it could increase the
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complexity of the algorithm.
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A sample query that finds a shortest path between two nodes can look like this:
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MATCH (a {id: 723})-[le *wShortest 10 (e, n | e.weight) total_weight]-(b {id: 882}) RETURN *
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This query has a upper bound length restriction set to `10`. This means that no
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path that traverses more than `10` edges will be considered as a valid result.
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#### Upper Bound Implications
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Since the upper bound parameter is optional, we can have different results based
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on this parameter.
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Lets take a look at the following graph and queries.
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```
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5 5
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/-----[1]-----\
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/ \
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/ \ 2
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[0] [4]---------[5]
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\ /
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\ /
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\--[2]---[3]--/
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3 3 3
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```
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MATCH (a {id: 0})-[le *wShortest 3 (e, n | e.weight) total_weight]-(b {id: 5}) RETURN *
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MATCH (a {id: 0})-[le *wShortest (e, n | e.weight) total_weight]-(b {id: 5}) RETURN *
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The first query will try to find the weighted shortest path between nodes `0`
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and `5` with the restriction on the path length set to `3`, and the second query
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will try to find the weighted shortest path with no restriction on the path
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length.
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The expected result for the first query is `0 -> 1 -> 4 -> 5` with total cost of
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`12`, while the expected result for the second query is `0 -> 2 -> 3 -> 4 -> 5`
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with total cost of `11`. Obviously, the second query can find the true shortest
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path because it has no restrictions on the length.
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To handle cases when the length restriction is set, *weighted shortest path*
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algorithm uses both vertex and distance as the state. This causes the search
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space to increase by the factor of the given upper bound. On the other hand, not
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setting the upper bound parameter, the search space might contain the whole
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graph.
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Because of this, one should always try to narrow down the upper bound limit to
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be as precise as possible in order to have a more performant query.
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@ -502,7 +502,7 @@ shortest path expansion:
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MATCH (a {id: 723})-[le *wShortest 10 (e, n | e.weight) total_weight]-(b {id: 882}) RETURN *
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The above query will find the shortest path of length up to 10 nodes between
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nodes `a` and `b`.
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nodes `a` and `b`. The length restriction parameter is optional.
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Weighted Shortest Path expansion allows an arbitrary expression that determines
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the weight for the current expansion. Total weight of a path is calculated as
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@ -5,7 +5,10 @@
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#include <queue>
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#include <random>
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#include <string>
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#include <tuple>
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#include <type_traits>
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#include <unordered_map>
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#include <unordered_set>
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#include <utility>
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#include "boost/archive/binary_iarchive.hpp"
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@ -25,6 +28,7 @@
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#include "query/path.hpp"
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#include "utils/algorithm.hpp"
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#include "utils/exceptions.hpp"
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#include "utils/hashing/fnv.hpp"
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DEFINE_HIDDEN_int32(remote_pull_sleep_micros, 10,
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"Sleep between remote result pulling in microseconds");
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@ -1212,10 +1216,15 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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ExpressionEvaluator evaluator(frame, context.parameters_,
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context.symbol_table_, db_,
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self_.graph_view_);
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// For the given (vertex, edge, vertex) tuple checks if they satisfy the
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// "where" condition. if so, places them in the priority queue.
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auto expand_pair = [this, &evaluator, &frame](
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VertexAccessor from, EdgeAccessor edge, VertexAccessor vertex) {
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auto create_state = [this](VertexAccessor vertex, int depth) {
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return std::make_pair(vertex, upper_bound_set_ ? depth : 0);
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};
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// For the given (edge, vertex, weight, depth) tuple checks if they
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// satisfy the "where" condition. if so, places them in the priority queue.
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auto expand_pair = [this, &evaluator, &frame, &create_state](
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EdgeAccessor edge, VertexAccessor vertex, double weight, int depth) {
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SwitchAccessor(edge, self_.graph_view_);
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SwitchAccessor(vertex, self_.graph_view_);
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@ -1240,28 +1249,29 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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throw QueryRuntimeException("Calculated weight can't be negative!");
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}
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auto total_weight = weights_[from] + typed_weight;
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auto found_it = weights_.find(vertex);
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if (found_it != weights_.end() &&
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found_it->second.Value<double>() <= total_weight.Value<double>())
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auto next_state = create_state(vertex, depth);
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auto next_weight = weight + typed_weight;
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auto found_it = total_cost_.find(next_state);
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if (found_it != total_cost_.end() &&
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found_it->second.Value<double>() <= next_weight.Value<double>())
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return;
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pq_.push(std::make_pair(std::make_pair(vertex, edge),
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total_weight.Value<double>()));
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pq_.push({next_weight.Value<double>(), depth + 1, vertex, edge});
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};
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// Populates the priority queue structure with expansions
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// from the given vertex. skips expansions that don't satisfy
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// the "where" condition.
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auto expand_from_vertex = [this, &expand_pair](VertexAccessor &vertex) {
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auto expand_from_vertex = [this, &expand_pair](VertexAccessor &vertex,
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double weight, int depth) {
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if (self_.direction_ != EdgeAtom::Direction::IN) {
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for (const EdgeAccessor &edge : vertex.out(&self_.edge_types_)) {
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expand_pair(vertex, edge, edge.to());
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expand_pair(edge, edge.to(), weight, depth);
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}
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}
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if (self_.direction_ != EdgeAtom::Direction::OUT) {
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for (const EdgeAccessor &edge : vertex.in(&self_.edge_types_)) {
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expand_pair(vertex, edge, edge.from());
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expand_pair(edge, edge.from(), weight, depth);
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}
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}
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};
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@ -1279,11 +1289,15 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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if (node.IsNull()) continue;
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}
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SwitchAccessor(vertex, self_.graph_view_);
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if (self_.upper_bound_) {
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upper_bound_ =
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self_.upper_bound_
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? EvaluateInt(evaluator, self_.upper_bound_,
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"Max depth in weighted shortest path expansion")
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: std::numeric_limits<int>::max();
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EvaluateInt(evaluator, self_.upper_bound_,
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"Max depth in weighted shortest path expansion");
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upper_bound_set_ = true;
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} else {
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upper_bound_ = std::numeric_limits<int>::max();
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upper_bound_set_ = false;
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}
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if (upper_bound_ < 1)
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throw QueryRuntimeException(
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"Max depth in weighted shortest path expansion must be greater "
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@ -1291,53 +1305,70 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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// Clear existing data structures.
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previous_.clear();
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weights_.clear();
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total_cost_.clear();
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yielded_vertices_.clear();
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pq_.push(std::make_pair(
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std::make_pair(vertex, std::experimental::nullopt), 0.0));
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pq_.push({0.0, 0, vertex, std::experimental::nullopt});
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// We are adding the starting vertex to the set of yielded vertices
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// because we don't want to yield paths that end with the starting
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// vertex.
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yielded_vertices_.insert(vertex);
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}
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while (!pq_.empty()) {
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auto current = pq_.top();
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double current_weight = std::get<0>(current);
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int current_depth = std::get<1>(current);
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VertexAccessor current_vertex = std::get<2>(current);
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std::experimental::optional<EdgeAccessor> current_edge =
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std::get<3>(current);
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pq_.pop();
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// Check if the edge has already been processed.
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if (weights_.find(current.first.first) != weights_.end()) {
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auto current_state = create_state(current_vertex, current_depth);
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// Check if the vertex has already been processed.
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if (total_cost_.find(current_state) != total_cost_.end()) {
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continue;
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}
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previous_.emplace(current.first.first, current.first.second);
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weights_.emplace(current.first.first, current.second);
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previous_.emplace(current_state, current_edge);
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total_cost_.emplace(current_state, current_weight);
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// Expand only if what we've just expanded is less than max depth.
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if (current_depth < upper_bound_)
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expand_from_vertex(current_vertex, current_weight, current_depth);
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// If we yielded a path for a vertex already, make the expansion but
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// don't return the path again.
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if (yielded_vertices_.find(current_vertex) != yielded_vertices_.end())
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continue;
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// Reconstruct the path.
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auto last_vertex = current.first.first;
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auto last_vertex = current_vertex;
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auto last_depth = current_depth;
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std::vector<TypedValue> edge_list{};
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while (true) {
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// Origin_vertex must be in previous.
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const auto &previous_edge = previous_.find(last_vertex)->second;
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const auto &previous_edge =
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previous_.find(create_state(last_vertex, last_depth))->second;
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if (!previous_edge) break;
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last_vertex = previous_edge->from() == last_vertex
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? previous_edge->to()
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: previous_edge->from();
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last_depth--;
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edge_list.push_back(previous_edge.value());
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}
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// Expand only if what we've just expanded is less then max depth.
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if (static_cast<int>(edge_list.size()) < upper_bound_)
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expand_from_vertex(current.first.first);
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if (edge_list.empty()) continue;
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// Place destination node on the frame, handle existence flag.
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if (self_.existing_node_) {
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TypedValue &node = frame[self_.node_symbol_];
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if ((node != current.first.first).Value<bool>())
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if ((node != current_vertex).Value<bool>())
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continue;
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else
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// Prevent expanding other paths, because we found the
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// shortest to existing node.
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ClearQueue();
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} else {
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frame[self_.node_symbol_] = current.first.first;
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frame[self_.node_symbol_] = current_vertex;
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}
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if (!self_.is_reverse_) {
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@ -1345,7 +1376,8 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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std::reverse(edge_list.begin(), edge_list.end());
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}
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frame[self_.edge_symbol_] = std::move(edge_list);
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frame[self_.total_weight_.value()] = current.second;
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frame[self_.total_weight_.value()] = current_weight;
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yielded_vertices_.insert(current_vertex);
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return true;
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}
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}
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@ -1354,7 +1386,8 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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void Reset() override {
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input_cursor_->Reset();
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previous_.clear();
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weights_.clear();
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total_cost_.clear();
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yielded_vertices_.clear();
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ClearQueue();
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}
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@ -1365,34 +1398,43 @@ class ExpandWeightedShortestPathCursor : public query::plan::Cursor {
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// Upper bound on the path length.
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int upper_bound_{-1};
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bool upper_bound_set_{false};
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struct WspStateHash {
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size_t operator()(const std::pair<VertexAccessor, int> &key) const {
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return HashCombine<VertexAccessor, int>{}(key.first, key.second);
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}
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};
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// Maps vertices to weights they got in expansion.
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std::unordered_map<VertexAccessor, TypedValue> weights_;
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std::unordered_map<std::pair<VertexAccessor, int>, TypedValue, WspStateHash>
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total_cost_;
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// Maps vertices to edges used to reach them.
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std::unordered_map<VertexAccessor, std::experimental::optional<EdgeAccessor>>
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std::unordered_map<std::pair<VertexAccessor, int>,
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std::experimental::optional<EdgeAccessor>, WspStateHash>
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previous_;
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// Keeps track of vertices for which we yielded a path already.
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std::unordered_set<VertexAccessor> yielded_vertices_;
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// Priority queue comparator. Keep lowest weight on top of the queue.
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class PriorityQueueComparator {
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public:
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bool operator()(
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const std::pair<std::pair<VertexAccessor,
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std::experimental::optional<EdgeAccessor>>,
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double> &lhs,
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const std::pair<std::pair<VertexAccessor,
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std::experimental::optional<EdgeAccessor>>,
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double> &rhs) {
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return lhs.second > rhs.second;
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const std::tuple<double, int, VertexAccessor,
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std::experimental::optional<EdgeAccessor>> &lhs,
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const std::tuple<double, int, VertexAccessor,
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std::experimental::optional<EdgeAccessor>> &rhs) {
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return std::get<0>(lhs) > std::get<0>(rhs);
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}
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};
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std::priority_queue<
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std::pair<
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std::pair<VertexAccessor, std::experimental::optional<EdgeAccessor>>,
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double>,
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std::vector<std::pair<
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std::pair<VertexAccessor, std::experimental::optional<EdgeAccessor>>,
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double>>,
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std::tuple<double, int, VertexAccessor,
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std::experimental::optional<EdgeAccessor>>,
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std::vector<std::tuple<double, int, VertexAccessor,
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std::experimental::optional<EdgeAccessor>>>,
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PriorityQueueComparator>
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pq_;
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@ -1108,9 +1108,10 @@ class QueryPlanExpandWeightedShortestPath : public testing::Test {
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for (auto &edge : e) edge.second.Reconstruct();
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}
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// defines and performs a breadth-first expansion with the given params
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// defines and performs a weighted shortest expansion with the given params
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// returns a vector of pairs. each pair is (vector-of-edges, vertex)
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auto ExpandWShortest(EdgeAtom::Direction direction, int max_depth,
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auto ExpandWShortest(EdgeAtom::Direction direction,
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std::experimental::optional<int> max_depth,
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Expression *where,
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GraphView graph_view = GraphView::AS_IS,
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std::experimental::optional<int> node_id = 0,
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@ -1137,7 +1138,8 @@ class QueryPlanExpandWeightedShortestPath : public testing::Test {
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auto filter_lambda = last_op = std::make_shared<ExpandVariable>(
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node_sym, edge_list_sym, EdgeAtom::Type::WEIGHTED_SHORTEST_PATH,
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direction, std::vector<storage::EdgeType>{}, false, nullptr,
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LITERAL(max_depth), last_op, n.sym_, existing_node_input != nullptr,
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max_depth ? LITERAL(max_depth.value()) : nullptr, last_op, n.sym_,
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existing_node_input != nullptr,
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ExpandVariable::Lambda{filter_edge, filter_node, where},
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ExpandVariable::Lambda{weight_edge, weight_node,
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PROPERTY_LOOKUP(ident_e, prop)},
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@ -1183,7 +1185,7 @@ class QueryPlanExpandWeightedShortestPath : public testing::Test {
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// / \
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// / 12 \ 2
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// [0]--------<--------[4]------->-------[5]
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// \ / (only for GraphState test)
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// \ / (on some tests only)
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// \ /
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// \->[2]->-[3]->/
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// 3 3 3
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@ -1324,6 +1326,40 @@ TEST_F(QueryPlanExpandWeightedShortestPath, ExistingNode) {
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}
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TEST_F(QueryPlanExpandWeightedShortestPath, UpperBound) {
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{
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auto results = ExpandWShortest(EdgeAtom::Direction::BOTH,
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std::experimental::nullopt, LITERAL(true));
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ASSERT_EQ(results.size(), 4);
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EXPECT_EQ(GetProp(results[0].vertex), 2);
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EXPECT_EQ(results[0].total_weight, 3);
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EXPECT_EQ(GetProp(results[1].vertex), 1);
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EXPECT_EQ(results[1].total_weight, 5);
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EXPECT_EQ(GetProp(results[2].vertex), 3);
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EXPECT_EQ(results[2].total_weight, 6);
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EXPECT_EQ(GetProp(results[3].vertex), 4);
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EXPECT_EQ(results[3].total_weight, 9);
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}
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{
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auto new_vertex = dba.InsertVertex();
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new_vertex.PropsSet(prop.second, 5);
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auto edge = dba.InsertEdge(v[4], new_vertex, edge_type);
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edge.PropsSet(prop.second, 2);
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auto results = ExpandWShortest(EdgeAtom::Direction::BOTH, 3, LITERAL(true),
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GraphView::NEW);
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ASSERT_EQ(results.size(), 5);
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EXPECT_EQ(GetProp(results[0].vertex), 2);
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EXPECT_EQ(results[0].total_weight, 3);
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EXPECT_EQ(GetProp(results[1].vertex), 1);
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EXPECT_EQ(results[1].total_weight, 5);
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EXPECT_EQ(GetProp(results[2].vertex), 3);
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EXPECT_EQ(results[2].total_weight, 6);
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EXPECT_EQ(GetProp(results[3].vertex), 4);
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EXPECT_EQ(results[3].total_weight, 9);
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EXPECT_EQ(GetProp(results[4].vertex), 5);
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EXPECT_EQ(results[4].total_weight, 12);
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}
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{
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auto results = ExpandWShortest(EdgeAtom::Direction::BOTH, 2, LITERAL(true));
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ASSERT_EQ(results.size(), 4);
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