package routing import ( "container/heap" "fmt" "math" "time" "github.com/btcsuite/btcd/btcec" "github.com/coreos/bbolt" "github.com/lightningnetwork/lnd/channeldb" "github.com/lightningnetwork/lnd/lnwire" "github.com/lightningnetwork/lnd/routing/route" "github.com/lightningnetwork/lnd/tlv" ) const ( // HopLimit is the maximum number hops that is permissible as a route. // Any potential paths found that lie above this limit will be rejected // with an error. This value is computed using the current fixed-size // packet length of the Sphinx construction. HopLimit = 20 // infinity is used as a starting distance in our shortest path search. infinity = math.MaxInt64 // RiskFactorBillionths controls the influence of time lock delta // of a channel on route selection. It is expressed as billionths // of msat per msat sent through the channel per time lock delta // block. See edgeWeight function below for more details. // The chosen value is based on the previous incorrect weight function // 1 + timelock + fee * fee. In this function, the fee penalty // diminishes the time lock penalty for all but the smallest amounts. // To not change the behaviour of path finding too drastically, a // relatively small value is chosen which is still big enough to give // some effect with smaller time lock values. The value may need // tweaking and/or be made configurable in the future. RiskFactorBillionths = 15 // estimatedNodeCount is used to preallocate the path finding structures // to avoid resizing and copies. It should be number on the same order as // the number of active nodes in the network. estimatedNodeCount = 10000 ) // pathFinder defines the interface of a path finding algorithm. type pathFinder = func(g *graphParams, r *RestrictParams, cfg *PathFindingConfig, source, target route.Vertex, amt lnwire.MilliSatoshi) ([]*channeldb.ChannelEdgePolicy, error) var ( // DefaultPaymentAttemptPenalty is the virtual cost in path finding weight // units of executing a payment attempt that fails. It is used to trade // off potentially better routes against their probability of // succeeding. DefaultPaymentAttemptPenalty = lnwire.NewMSatFromSatoshis(100) // DefaultMinRouteProbability is the default minimum probability for routes // returned from findPath. DefaultMinRouteProbability = float64(0.01) // DefaultAprioriHopProbability is the default a priori probability for // a hop. DefaultAprioriHopProbability = float64(0.6) ) // edgePolicyWithSource is a helper struct to keep track of the source node // of a channel edge. ChannelEdgePolicy only contains to destination node // of the edge. type edgePolicyWithSource struct { sourceNode route.Vertex edge *channeldb.ChannelEdgePolicy } // newRoute returns a fully valid route between the source and target that's // capable of supporting a payment of `amtToSend` after fees are fully // computed. If the route is too long, or the selected path cannot support the // fully payment including fees, then a non-nil error is returned. // // NOTE: The passed slice of ChannelHops MUST be sorted in forward order: from // the source to the target node of the path finding attempt. func newRoute(amtToSend lnwire.MilliSatoshi, sourceVertex route.Vertex, pathEdges []*channeldb.ChannelEdgePolicy, currentHeight uint32, finalCLTVDelta uint16, finalDestRecords []tlv.Record) (*route.Route, error) { var ( hops []*route.Hop // totalTimeLock will accumulate the cumulative time lock // across the entire route. This value represents how long the // sender will need to wait in the *worst* case. totalTimeLock = currentHeight // nextIncomingAmount is the amount that will need to flow into // the *next* hop. Since we're going to be walking the route // backwards below, this next hop gets closer and closer to the // sender of the payment. nextIncomingAmount lnwire.MilliSatoshi ) pathLength := len(pathEdges) for i := pathLength - 1; i >= 0; i-- { // Now we'll start to calculate the items within the per-hop // payload for the hop this edge is leading to. edge := pathEdges[i] // If this is the last hop, then the hop payload will contain // the exact amount. In BOLT #4: Onion Routing // Protocol / "Payload for the Last Node", this is detailed. amtToForward := amtToSend // Fee is not part of the hop payload, but only used for // reporting through RPC. Set to zero for the final hop. fee := lnwire.MilliSatoshi(0) // If the current hop isn't the last hop, then add enough funds // to pay for transit over the next link. if i != len(pathEdges)-1 { // The amount that the current hop needs to forward is // equal to the incoming amount of the next hop. amtToForward = nextIncomingAmount // The fee that needs to be paid to the current hop is // based on the amount that this hop needs to forward // and its policy for the outgoing channel. This policy // is stored as part of the incoming channel of // the next hop. fee = pathEdges[i+1].ComputeFee(amtToForward) } // If this is the last hop, then for verification purposes, the // value of the outgoing time-lock should be _exactly_ the // absolute time out they'd expect in the HTLC. var outgoingTimeLock uint32 if i == len(pathEdges)-1 { // As this is the last hop, we'll use the specified // final CLTV delta value instead of the value from the // last link in the route. totalTimeLock += uint32(finalCLTVDelta) outgoingTimeLock = currentHeight + uint32(finalCLTVDelta) } else { // Next, increment the total timelock of the entire // route such that each hops time lock increases as we // walk backwards in the route, using the delta of the // previous hop. delta := uint32(pathEdges[i+1].TimeLockDelta) totalTimeLock += delta // Otherwise, the value of the outgoing time-lock will // be the value of the time-lock for the _outgoing_ // HTLC, so we factor in their specified grace period // (time lock delta). outgoingTimeLock = totalTimeLock - delta } // Since we're traversing the path backwards atm, we prepend // each new hop such that, the final slice of hops will be in // the forwards order. currentHop := &route.Hop{ PubKeyBytes: edge.Node.PubKeyBytes, ChannelID: edge.ChannelID, AmtToForward: amtToForward, OutgoingTimeLock: outgoingTimeLock, LegacyPayload: true, } // We start out above by assuming that this node needs the // legacy payload, as if we don't have the full // NodeAnnouncement information for this node, then we can't // assume it knows the latest features. If we do have a feature // vector for this node, then we'll update the info now. if edge.Node.Features != nil { features := edge.Node.Features currentHop.LegacyPayload = !features.HasFeature( lnwire.TLVOnionPayloadOptional, ) } // If this is the last hop, then we'll populate any TLV records // destined for it. if i == len(pathEdges)-1 && len(finalDestRecords) != 0 { currentHop.TLVRecords = finalDestRecords } hops = append([]*route.Hop{currentHop}, hops...) // Finally, we update the amount that needs to flow into the // *next* hop, which is the amount this hop needs to forward, // accounting for the fee that it takes. nextIncomingAmount = amtToForward + fee } // With the base routing data expressed as hops, build the full route newRoute, err := route.NewRouteFromHops( nextIncomingAmount, totalTimeLock, route.Vertex(sourceVertex), hops, ) if err != nil { return nil, err } return newRoute, nil } // edgeWeight computes the weight of an edge. This value is used when searching // for the shortest path within the channel graph between two nodes. Weight is // is the fee itself plus a time lock penalty added to it. This benefits // channels with shorter time lock deltas and shorter (hops) routes in general. // RiskFactor controls the influence of time lock on route selection. This is // currently a fixed value, but might be configurable in the future. func edgeWeight(lockedAmt lnwire.MilliSatoshi, fee lnwire.MilliSatoshi, timeLockDelta uint16) int64 { // timeLockPenalty is the penalty for the time lock delta of this channel. // It is controlled by RiskFactorBillionths and scales proportional // to the amount that will pass through channel. Rationale is that it if // a twice as large amount gets locked up, it is twice as bad. timeLockPenalty := int64(lockedAmt) * int64(timeLockDelta) * RiskFactorBillionths / 1000000000 return int64(fee) + timeLockPenalty } // graphParams wraps the set of graph parameters passed to findPath. type graphParams struct { // tx can be set to an existing db transaction. If not set, a new // transaction will be started. tx *bbolt.Tx // graph is the ChannelGraph to be used during path finding. graph *channeldb.ChannelGraph // additionalEdges is an optional set of edges that should be // considered during path finding, that is not already found in the // channel graph. additionalEdges map[route.Vertex][]*channeldb.ChannelEdgePolicy // bandwidthHints is an optional map from channels to bandwidths that // can be populated if the caller has a better estimate of the current // channel bandwidth than what is found in the graph. If set, it will // override the capacities and disabled flags found in the graph for // local channels when doing path finding. In particular, it should be // set to the current available sending bandwidth for active local // channels, and 0 for inactive channels. bandwidthHints map[uint64]lnwire.MilliSatoshi } // RestrictParams wraps the set of restrictions passed to findPath that the // found path must adhere to. type RestrictParams struct { // ProbabilitySource is a callback that is expected to return the // success probability of traversing the channel from the node. ProbabilitySource func(route.Vertex, route.Vertex, lnwire.MilliSatoshi) float64 // FeeLimit is a maximum fee amount allowed to be used on the path from // the source to the target. FeeLimit lnwire.MilliSatoshi // OutgoingChannelID is the channel that needs to be taken to the first // hop. If nil, any channel may be used. OutgoingChannelID *uint64 // LastHop is the pubkey of the last node before the final destination // is reached. If nil, any node may be used. LastHop *route.Vertex // CltvLimit is the maximum time lock of the route excluding the final // ctlv. After path finding is complete, the caller needs to increase // all cltv expiry heights with the required final cltv delta. CltvLimit uint32 // DestPayloadTLV should be set to true if we need to drop off a TLV // payload at the final hop in order to properly complete this payment // attempt. DestPayloadTLV bool } // PathFindingConfig defines global parameters that control the trade-off in // path finding between fees and probabiity. type PathFindingConfig struct { // PaymentAttemptPenalty is the virtual cost in path finding weight // units of executing a payment attempt that fails. It is used to trade // off potentially better routes against their probability of // succeeding. PaymentAttemptPenalty lnwire.MilliSatoshi // MinProbability defines the minimum success probability of the // returned route. MinProbability float64 } // findPath attempts to find a path from the source node within the // ChannelGraph to the target node that's capable of supporting a payment of // `amt` value. The current approach implemented is modified version of // Dijkstra's algorithm to find a single shortest path between the source node // and the destination. The distance metric used for edges is related to the // time-lock+fee costs along a particular edge. If a path is found, this // function returns a slice of ChannelHop structs which encoded the chosen path // from the target to the source. The search is performed backwards from // destination node back to source. This is to properly accumulate fees // that need to be paid along the path and accurately check the amount // to forward at every node against the available bandwidth. func findPath(g *graphParams, r *RestrictParams, cfg *PathFindingConfig, source, target route.Vertex, amt lnwire.MilliSatoshi) ( []*channeldb.ChannelEdgePolicy, error) { // Pathfinding can be a significant portion of the total payment // latency, especially on low-powered devices. Log several metrics to // aid in the analysis performance problems in this area. start := time.Now() nodesVisited := 0 edgesExpanded := 0 defer func() { timeElapsed := time.Since(start) log.Debugf("Pathfinding perf metrics: nodes=%v, edges=%v, "+ "time=%v", nodesVisited, edgesExpanded, timeElapsed) }() var err error tx := g.tx if tx == nil { tx, err = g.graph.Database().Begin(false) if err != nil { return nil, err } defer tx.Rollback() } if r.DestPayloadTLV { // Check if the target has TLV enabled targetKey, err := btcec.ParsePubKey(target[:], btcec.S256()) if err != nil { return nil, err } targetNode, err := g.graph.FetchLightningNode(targetKey) if err != nil { return nil, err } if targetNode.Features != nil { supportsTLV := targetNode.Features.HasFeature( lnwire.TLVOnionPayloadOptional, ) if !supportsTLV { return nil, fmt.Errorf("destination hop doesn't " + "understand new TLV paylods") } } } // First we'll initialize an empty heap which'll help us to quickly // locate the next edge we should visit next during our graph // traversal. nodeHeap := newDistanceHeap(estimatedNodeCount) // Holds the current best distance for a given node. distance := make(map[route.Vertex]*nodeWithDist, estimatedNodeCount) additionalEdgesWithSrc := make(map[route.Vertex][]*edgePolicyWithSource) for vertex, outgoingEdgePolicies := range g.additionalEdges { // Build reverse lookup to find incoming edges. Needed because // search is taken place from target to source. for _, outgoingEdgePolicy := range outgoingEdgePolicies { toVertex := outgoingEdgePolicy.Node.PubKeyBytes incomingEdgePolicy := &edgePolicyWithSource{ sourceNode: vertex, edge: outgoingEdgePolicy, } additionalEdgesWithSrc[toVertex] = append(additionalEdgesWithSrc[toVertex], incomingEdgePolicy) } } // We can't always assume that the end destination is publicly // advertised to the network so we'll manually include the target node. // The target node charges no fee. Distance is set to 0, because this is // the starting point of the graph traversal. We are searching backwards // to get the fees first time right and correctly match channel // bandwidth. // // Don't record the initial partial path in the distance map and reserve // that key for the source key in the case we route to ourselves. partialPath := &nodeWithDist{ dist: 0, weight: 0, node: target, amountToReceive: amt, incomingCltv: 0, probability: 1, } // processEdge is a helper closure that will be used to make sure edges // satisfy our specific requirements. processEdge := func(fromVertex route.Vertex, edge *channeldb.ChannelEdgePolicy, toNodeDist *nodeWithDist) { edgesExpanded++ // Calculate amount that the candidate node would have to sent // out. amountToSend := toNodeDist.amountToReceive // Request the success probability for this edge. edgeProbability := r.ProbabilitySource( fromVertex, toNodeDist.node, amountToSend, ) log.Trace(newLogClosure(func() string { return fmt.Sprintf("path finding probability: fromnode=%v,"+ " tonode=%v, probability=%v", fromVertex, toNodeDist.node, edgeProbability) })) // If the probability is zero, there is no point in trying. if edgeProbability == 0 { return } // Compute fee that fromVertex is charging. It is based on the // amount that needs to be sent to the next node in the route. // // Source node has no predecessor to pay a fee. Therefore set // fee to zero, because it should not be included in the fee // limit check and edge weight. // // Also determine the time lock delta that will be added to the // route if fromVertex is selected. If fromVertex is the source // node, no additional timelock is required. var fee lnwire.MilliSatoshi var timeLockDelta uint16 if fromVertex != source { fee = edge.ComputeFee(amountToSend) timeLockDelta = edge.TimeLockDelta } incomingCltv := toNodeDist.incomingCltv + uint32(timeLockDelta) // Check that we are within our CLTV limit. if incomingCltv > r.CltvLimit { return } // amountToReceive is the amount that the node that is added to // the distance map needs to receive from a (to be found) // previous node in the route. That previous node will need to // pay the amount that this node forwards plus the fee it // charges. amountToReceive := amountToSend + fee // Check if accumulated fees would exceed fee limit when this // node would be added to the path. totalFee := amountToReceive - amt if totalFee > r.FeeLimit { return } // Calculate total probability of successfully reaching target // by multiplying the probabilities. Both this edge and the rest // of the route must succeed. probability := toNodeDist.probability * edgeProbability // If the probability is below the specified lower bound, we can // abandon this direction. Adding further nodes can only lower // the probability more. if probability < cfg.MinProbability { return } // By adding fromVertex in the route, there will be an extra // weight composed of the fee that this node will charge and // the amount that will be locked for timeLockDelta blocks in // the HTLC that is handed out to fromVertex. weight := edgeWeight(amountToReceive, fee, timeLockDelta) // Compute the tentative weight to this new channel/edge // which is the weight from our toNode to the target node // plus the weight of this edge. tempWeight := toNodeDist.weight + weight // Add an extra factor to the weight to take into account the // probability. tempDist := getProbabilityBasedDist( tempWeight, probability, int64(cfg.PaymentAttemptPenalty), ) // If the current best route is better than this candidate // route, return. It is important to also return if the distance // is equal, because otherwise the algorithm could run into an // endless loop. current, ok := distance[fromVertex] if ok && tempDist >= current.dist { return } // Every edge should have a positive time lock delta. If we // encounter a zero delta, log a warning line. if edge.TimeLockDelta == 0 { log.Warnf("Channel %v has zero cltv delta", edge.ChannelID) } // All conditions are met and this new tentative distance is // better than the current best known distance to this node. // The new better distance is recorded, and also our "next hop" // map is populated with this edge. withDist := &nodeWithDist{ dist: tempDist, weight: tempWeight, node: fromVertex, amountToReceive: amountToReceive, incomingCltv: incomingCltv, probability: probability, nextHop: edge, } distance[fromVertex] = withDist // Either push withDist onto the heap if the node // represented by fromVertex is not already on the heap OR adjust // its position within the heap via heap.Fix. nodeHeap.PushOrFix(withDist) } // TODO(roasbeef): also add path caching // * similar to route caching, but doesn't factor in the amount routeToSelf := source == target for { nodesVisited++ pivot := partialPath.node // Create unified policies for all incoming connections. u := newUnifiedPolicies(source, pivot, r.OutgoingChannelID) err := u.addGraphPolicies(g.graph, tx) if err != nil { return nil, err } for _, reverseEdge := range additionalEdgesWithSrc[pivot] { u.addPolicy(reverseEdge.sourceNode, reverseEdge.edge, 0) } amtToSend := partialPath.amountToReceive // Expand all connections using the optimal policy for each // connection. for fromNode, unifiedPolicy := range u.policies { // The target node is not recorded in the distance map. // Therefore we need to have this check to prevent // creating a cycle. Only when we intend to route to // self, we allow this cycle to form. In that case we'll // also break out of the search loop below. if !routeToSelf && fromNode == target { continue } // Apply last hop restriction if set. if r.LastHop != nil && pivot == target && fromNode != *r.LastHop { continue } policy := unifiedPolicy.getPolicy( amtToSend, g.bandwidthHints, ) if policy == nil { continue } // Check if this candidate node is better than what we // already have. processEdge(fromNode, policy, partialPath) } if nodeHeap.Len() == 0 { break } // Fetch the node within the smallest distance from our source // from the heap. partialPath = heap.Pop(&nodeHeap).(*nodeWithDist) // If we've reached our source (or we don't have any incoming // edges), then we're done here and can exit the graph // traversal early. if partialPath.node == source { break } } // Use the distance map to unravel the forward path from source to // target. var pathEdges []*channeldb.ChannelEdgePolicy currentNode := source for { // Determine the next hop forward using the next map. currentNodeWithDist, ok := distance[currentNode] if !ok { // If the node doesnt have a next hop it means we didn't find a path. return nil, newErrf(ErrNoPathFound, "unable to find a "+ "path to destination") } // Add the next hop to the list of path edges. pathEdges = append(pathEdges, currentNodeWithDist.nextHop) // Advance current node. currentNode = currentNodeWithDist.nextHop.Node.PubKeyBytes // Check stop condition at the end of this loop. This prevents // breaking out too soon for self-payments that have target set // to source. if currentNode == target { break } } // The route is invalid if it spans more than 20 hops. The current // Sphinx (onion routing) implementation can only encode up to 20 hops // as the entire packet is fixed size. If this route is more than 20 // hops, then it's invalid. numEdges := len(pathEdges) if numEdges > HopLimit { return nil, newErr(ErrMaxHopsExceeded, "potential path has "+ "too many hops") } log.Debugf("Found route: probability=%v, hops=%v, fee=%v\n", distance[source].probability, numEdges, distance[source].amountToReceive-amt) return pathEdges, nil } // getProbabilityBasedDist converts a weight into a distance that takes into // account the success probability and the (virtual) cost of a failed payment // attempt. // // Derivation: // // Suppose there are two routes A and B with fees Fa and Fb and success // probabilities Pa and Pb. // // Is the expected cost of trying route A first and then B lower than trying the // other way around? // // The expected cost of A-then-B is: Pa*Fa + (1-Pa)*Pb*(c+Fb) // // The expected cost of B-then-A is: Pb*Fb + (1-Pb)*Pa*(c+Fa) // // In these equations, the term representing the case where both A and B fail is // left out because its value would be the same in both cases. // // Pa*Fa + (1-Pa)*Pb*(c+Fb) < Pb*Fb + (1-Pb)*Pa*(c+Fa) // // Pa*Fa + Pb*c + Pb*Fb - Pa*Pb*c - Pa*Pb*Fb < Pb*Fb + Pa*c + Pa*Fa - Pa*Pb*c - Pa*Pb*Fa // // Removing terms that cancel out: // Pb*c - Pa*Pb*Fb < Pa*c - Pa*Pb*Fa // // Divide by Pa*Pb: // c/Pa - Fb < c/Pb - Fa // // Move terms around: // Fa + c/Pa < Fb + c/Pb // // So the value of F + c/P can be used to compare routes. func getProbabilityBasedDist(weight int64, probability float64, penalty int64) int64 { // Clamp probability to prevent overflow. const minProbability = 0.00001 if probability < minProbability { return infinity } return weight + int64(float64(penalty)/probability) }