package routing import ( "bytes" "encoding/binary" "fmt" "math" "container/heap" "github.com/btcsuite/btcd/btcec" "github.com/coreos/bbolt" "github.com/lightningnetwork/lightning-onion" "github.com/lightningnetwork/lnd/channeldb" "github.com/lightningnetwork/lnd/lnwire" ) 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 ) // HopHint is a routing hint that contains the minimum information of a channel // required for an intermediate hop in a route to forward the payment to the // next. This should be ideally used for private channels, since they are not // publicly advertised to the network for routing. type HopHint struct { // NodeID is the public key of the node at the start of the channel. NodeID *btcec.PublicKey // ChannelID is the unique identifier of the channel. ChannelID uint64 // FeeBaseMSat is the base fee of the channel in millisatoshis. FeeBaseMSat uint32 // FeeProportionalMillionths is the fee rate, in millionths of a // satoshi, for every satoshi sent through the channel. FeeProportionalMillionths uint32 // CLTVExpiryDelta is the time-lock delta of the channel. CLTVExpiryDelta uint16 } // Hop represents an intermediate or final node of the route. This naming // is in line with the definition given in BOLT #4: Onion Routing Protocol. // The struct houses the channel along which this hop can be reached and // the values necessary to create the HTLC that needs to be sent to the // next hop. It is also used to encode the per-hop payload included within // the Sphinx packet. type Hop struct { // PubKeyBytes is the raw bytes of the public key of the target node. PubKeyBytes Vertex // ChannelID is the unique channel ID for the channel. The first 3 // bytes are the block height, the next 3 the index within the block, // and the last 2 bytes are the output index for the channel. ChannelID uint64 // OutgoingTimeLock is the timelock value that should be used when // crafting the _outgoing_ HTLC from this hop. OutgoingTimeLock uint32 // AmtToForward is the amount that this hop will forward to the next // hop. This value is less than the value that the incoming HTLC // carries as a fee will be subtracted by the hop. AmtToForward lnwire.MilliSatoshi } // 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 *channeldb.LightningNode edge *channeldb.ChannelEdgePolicy } // computeFee computes the fee to forward an HTLC of `amt` milli-satoshis over // the passed active payment channel. This value is currently computed as // specified in BOLT07, but will likely change in the near future. func computeFee(amt lnwire.MilliSatoshi, edge *channeldb.ChannelEdgePolicy) lnwire.MilliSatoshi { return edge.FeeBaseMSat + (amt*edge.FeeProportionalMillionths)/1000000 } // isSamePath returns true if path1 and path2 travel through the exact same // edges, and false otherwise. func isSamePath(path1, path2 []*channeldb.ChannelEdgePolicy) bool { if len(path1) != len(path2) { return false } for i := 0; i < len(path1); i++ { if path1[i].ChannelID != path2[i].ChannelID { return false } } return true } // Route represents a path through the channel graph which runs over one or // more channels in succession. This struct carries all the information // required to craft the Sphinx onion packet, and send the payment along the // first hop in the path. A route is only selected as valid if all the channels // have sufficient capacity to carry the initial payment amount after fees are // accounted for. type Route struct { // TotalTimeLock is the cumulative (final) time lock across the entire // route. This is the CLTV value that should be extended to the first // hop in the route. All other hops will decrement the time-lock as // advertised, leaving enough time for all hops to wait for or present // the payment preimage to complete the payment. TotalTimeLock uint32 // TotalFees is the sum of the fees paid at each hop within the final // route. In the case of a one-hop payment, this value will be zero as // we don't need to pay a fee to ourself. TotalFees lnwire.MilliSatoshi // TotalAmount is the total amount of funds required to complete a // payment over this route. This value includes the cumulative fees at // each hop. As a result, the HTLC extended to the first-hop in the // route will need to have at least this many satoshis, otherwise the // route will fail at an intermediate node due to an insufficient // amount of fees. TotalAmount lnwire.MilliSatoshi // Hops contains details concerning the specific forwarding details at // each hop. Hops []*Hop // nodeIndex is a map that allows callers to quickly look up if a node // is present in this computed route or not. nodeIndex map[Vertex]struct{} // chanIndex is an index that allows callers to determine if a channel // is present in this route or not. Channels are identified by the // uint64 version of the short channel ID. chanIndex map[uint64]struct{} // nextHop maps a node, to the next channel that it will pass the HTLC // off to. With this map, we can easily look up the next outgoing // channel or node for pruning purposes. nextHopMap map[Vertex]*Hop // prevHop maps a node, to the channel that was directly before it // within the route. With this map, we can easily look up the previous // channel or node for pruning purposes. prevHopMap map[Vertex]*Hop } // HopFee returns the fee charged by the route hop indicated by hopIndex. func (r *Route) HopFee(hopIndex int) lnwire.MilliSatoshi { var incomingAmt lnwire.MilliSatoshi if hopIndex == 0 { incomingAmt = r.TotalAmount } else { incomingAmt = r.Hops[hopIndex-1].AmtToForward } // Fee is calculated as difference between incoming and outgoing amount. return incomingAmt - r.Hops[hopIndex].AmtToForward } // nextHopVertex returns the next hop (by Vertex) after the target node. If the // target node is not found in the route, then false is returned. func (r *Route) nextHopVertex(n *btcec.PublicKey) (Vertex, bool) { hop, ok := r.nextHopMap[NewVertex(n)] return Vertex(hop.PubKeyBytes), ok } // nextHopChannel returns the uint64 channel ID of the next hop after the // target node. If the target node is not found in the route, then false is // returned. func (r *Route) nextHopChannel(n *btcec.PublicKey) (*Hop, bool) { hop, ok := r.nextHopMap[NewVertex(n)] return hop, ok } // prevHopChannel returns the uint64 channel ID of the before hop after the // target node. If the target node is not found in the route, then false is // returned. func (r *Route) prevHopChannel(n *btcec.PublicKey) (*Hop, bool) { hop, ok := r.prevHopMap[NewVertex(n)] return hop, ok } // containsNode returns true if a node is present in the target route, and // false otherwise. func (r *Route) containsNode(v Vertex) bool { _, ok := r.nodeIndex[v] return ok } // containsChannel returns true if a channel is present in the target route, // and false otherwise. The passed chanID should be the converted uint64 form // of lnwire.ShortChannelID. func (r *Route) containsChannel(chanID uint64) bool { _, ok := r.chanIndex[chanID] return ok } // ToHopPayloads converts a complete route into the series of per-hop payloads // that is to be encoded within each HTLC using an opaque Sphinx packet. func (r *Route) ToHopPayloads() []sphinx.HopData { hopPayloads := make([]sphinx.HopData, len(r.Hops)) // For each hop encoded within the route, we'll convert the hop struct // to the matching per-hop payload struct as used by the sphinx // package. for i, hop := range r.Hops { hopPayloads[i] = sphinx.HopData{ // TODO(roasbeef): properly set realm, make sphinx type // an enum actually? Realm: 0, ForwardAmount: uint64(hop.AmtToForward), OutgoingCltv: hop.OutgoingTimeLock, } // As a base case, the next hop is set to all zeroes in order // to indicate that the "last hop" as no further hops after it. nextHop := uint64(0) // If we aren't on the last hop, then we set the "next address" // field to be the channel that directly follows it. if i != len(r.Hops)-1 { nextHop = r.Hops[i+1].ChannelID } binary.BigEndian.PutUint64(hopPayloads[i].NextAddress[:], nextHop) } return hopPayloads } // 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, feeLimit lnwire.MilliSatoshi, sourceVertex Vertex, pathEdges []*channeldb.ChannelEdgePolicy, currentHeight uint32, finalCLTVDelta uint16) (*Route, error) { var ( hops []*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 = computeFee(amtToForward, pathEdges[i+1]) } // 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 := &Hop{ PubKeyBytes: Vertex(edge.Node.PubKeyBytes), ChannelID: edge.ChannelID, AmtToForward: amtToForward, OutgoingTimeLock: outgoingTimeLock, } hops = append([]*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 := NewRouteFromHops( nextIncomingAmount, totalTimeLock, sourceVertex, hops, ) // Invalidate this route if its total fees exceed our fee limit. if newRoute.TotalFees > feeLimit { err := fmt.Sprintf("total route fees exceeded fee "+ "limit of %v", feeLimit) return nil, newErrf(ErrFeeLimitExceeded, err) } return newRoute, nil } // NewRouteFromHops creates a new Route structure from the minimally required // information to perform the payment. It infers fee amounts and populates the // node, chan and prev/next hop maps. func NewRouteFromHops(amtToSend lnwire.MilliSatoshi, timeLock uint32, sourceVertex Vertex, hops []*Hop) *Route { // First, we'll create a route struct and populate it with the fields // for which the values are provided as arguments of this function. // TotalFees is determined based on the difference between the amount // that is send from the source and the final amount that is received // by the destination. route := &Route{ Hops: hops, TotalTimeLock: timeLock, TotalAmount: amtToSend, TotalFees: amtToSend - hops[len(hops)-1].AmtToForward, nodeIndex: make(map[Vertex]struct{}), chanIndex: make(map[uint64]struct{}), nextHopMap: make(map[Vertex]*Hop), prevHopMap: make(map[Vertex]*Hop), } // Then we'll update the node and channel index, to indicate that this // Vertex and incoming channel link are present within this route. // Also, the prev and next hop maps will be populated. prevNode := sourceVertex for i := 0; i < len(hops); i++ { hop := hops[i] v := Vertex(hop.PubKeyBytes) route.nodeIndex[v] = struct{}{} route.chanIndex[hop.ChannelID] = struct{}{} route.prevHopMap[v] = hop route.nextHopMap[prevNode] = hop prevNode = v } return route } // Vertex is a simple alias for the serialization of a compressed Bitcoin // public key. type Vertex [33]byte // NewVertex returns a new Vertex given a public key. func NewVertex(pub *btcec.PublicKey) Vertex { var v Vertex copy(v[:], pub.SerializeCompressed()) return v } // String returns a human readable version of the Vertex which is the // hex-encoding of the serialized compressed public key. func (v Vertex) String() string { return fmt.Sprintf("%x", v[:]) } // 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 } // 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(tx *bolt.Tx, graph *channeldb.ChannelGraph, additionalEdges map[Vertex][]*channeldb.ChannelEdgePolicy, sourceNode *channeldb.LightningNode, target *btcec.PublicKey, ignoredNodes map[Vertex]struct{}, ignoredEdges map[uint64]struct{}, amt lnwire.MilliSatoshi, feeLimit lnwire.MilliSatoshi, bandwidthHints map[uint64]lnwire.MilliSatoshi) ([]*channeldb.ChannelEdgePolicy, error) { var err error if tx == nil { tx, err = graph.Database().Begin(false) if err != nil { return nil, err } defer tx.Rollback() } // 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. var nodeHeap distanceHeap // For each node in the graph, we create an entry in the distance map // for the node set with a distance of "infinity". graph.ForEachNode // also returns the source node, so there is no need to add the source // node explicitly. distance := make(map[Vertex]nodeWithDist) if err := graph.ForEachNode(tx, func(_ *bolt.Tx, node *channeldb.LightningNode) error { // TODO(roasbeef): with larger graph can just use disk seeks // with a visited map distance[Vertex(node.PubKeyBytes)] = nodeWithDist{ dist: infinity, node: node, } return nil }); err != nil { return nil, err } additionalEdgesWithSrc := make(map[Vertex][]*edgePolicyWithSource) for vertex, outgoingEdgePolicies := range additionalEdges { // We'll also include all the nodes found within the additional // edges that are not known to us yet in the distance map. node := &channeldb.LightningNode{PubKeyBytes: vertex} distance[vertex] = nodeWithDist{ dist: infinity, node: node, } // 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: node, edge: outgoingEdgePolicy, } additionalEdgesWithSrc[toVertex] = append(additionalEdgesWithSrc[toVertex], incomingEdgePolicy) } } sourceVertex := Vertex(sourceNode.PubKeyBytes) // We can't always assume that the end destination is publicly // advertised to the network and included in the graph.ForEachNode call // above, 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. targetVertex := NewVertex(target) targetNode := &channeldb.LightningNode{PubKeyBytes: targetVertex} distance[targetVertex] = nodeWithDist{ dist: 0, node: targetNode, amountToReceive: amt, fee: 0, } // We'll use this map as a series of "next" hop pointers. So to get // from `Vertex` to the target node, we'll take the edge that it's // mapped to within `next`. next := make(map[Vertex]*channeldb.ChannelEdgePolicy) // processEdge is a helper closure that will be used to make sure edges // satisfy our specific requirements. processEdge := func(fromNode *channeldb.LightningNode, edge *channeldb.ChannelEdgePolicy, bandwidth lnwire.MilliSatoshi, toNode Vertex) { fromVertex := Vertex(fromNode.PubKeyBytes) // If the edge is currently disabled, then we'll stop here, as // we shouldn't attempt to route through it. edgeFlags := lnwire.ChanUpdateFlag(edge.Flags) if edgeFlags&lnwire.ChanUpdateDisabled != 0 { return } // If this vertex or edge has been black listed, then we'll // skip exploring this edge. if _, ok := ignoredNodes[fromVertex]; ok { return } if _, ok := ignoredEdges[edge.ChannelID]; ok { return } toNodeDist := distance[toNode] amountToSend := toNodeDist.amountToReceive // If the estimated band width of the channel edge is not able // to carry the amount that needs to be send, return. if bandwidth < amountToSend { return } // If the amountToSend is less than the minimum required // amount, return. if amountToSend < edge.MinHTLC { return } // Compute fee that fromNode 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 fromNode is selected. If fromNode is the source // node, no additional timelock is required. var fee lnwire.MilliSatoshi var timeLockDelta uint16 if fromVertex != sourceVertex { fee = computeFee(amountToSend, edge) timeLockDelta = edge.TimeLockDelta } // 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 > feeLimit { return } // By adding fromNode 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 fromNode. weight := edgeWeight(amountToReceive, fee, timeLockDelta) // Compute the tentative distance to this new channel/edge // which is the distance from our toNode to the target node // plus the weight of this edge. tempDist := toNodeDist.dist + weight // If this new tentative distance is not better than the current // best known distance to this node, return. if tempDist >= distance[fromVertex].dist { return } // If the edge has no time lock delta, the payment will always // fail, so return. // // TODO(joostjager): Is this really true? Can't it be that // nodes take this risk in exchange for a extraordinary high // fee? if edge.TimeLockDelta == 0 { return } // 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. distance[fromVertex] = nodeWithDist{ dist: tempDist, node: fromNode, amountToReceive: amountToReceive, fee: fee, } next[fromVertex] = edge // Add this new node to our heap as we'd like to further // explore backwards through this edge. heap.Push(&nodeHeap, distance[fromVertex]) } // TODO(roasbeef): also add path caching // * similar to route caching, but doesn't factor in the amount // To start, our target node will the sole item within our distance // heap. heap.Push(&nodeHeap, distance[targetVertex]) for nodeHeap.Len() != 0 { // Fetch the node within the smallest distance from our source // from the heap. partialPath := heap.Pop(&nodeHeap).(nodeWithDist) bestNode := partialPath.node // 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 bytes.Equal(bestNode.PubKeyBytes[:], sourceVertex[:]) { break } // Now that we've found the next potential step to take we'll // examine all the incoming edges (channels) from this node to // further our graph traversal. pivot := Vertex(bestNode.PubKeyBytes) err := bestNode.ForEachChannel(tx, func(tx *bolt.Tx, edgeInfo *channeldb.ChannelEdgeInfo, _, inEdge *channeldb.ChannelEdgePolicy) error { // If there is no edge policy for this candidate // node, skip. Note that we are searching backwards // so this node would have come prior to the pivot // node in the route. if inEdge == nil { return nil } // We'll query the lower layer to see if we can obtain // any more up to date information concerning the // bandwidth of this edge. edgeBandwidth, ok := bandwidthHints[edgeInfo.ChannelID] if !ok { // If we don't have a hint for this edge, then // we'll just use the known Capacity as the // available bandwidth. edgeBandwidth = lnwire.NewMSatFromSatoshis( edgeInfo.Capacity, ) } // Before we can process the edge, we'll need to fetch // the node on the _other_ end of this channel as we // may later need to iterate over the incoming edges of // this node if we explore it further. channelSource, err := edgeInfo.FetchOtherNode( tx, pivot[:], ) if err != nil { return err } // Check if this candidate node is better than what we // already have. processEdge(channelSource, inEdge, edgeBandwidth, pivot) return nil }) if err != nil { return nil, err } // Then, we'll examine all the additional edges from the node // we're currently visiting. Since we don't know the capacity // of the private channel, we'll assume it was selected as a // routing hint due to having enough capacity for the payment // and use the payment amount as its capacity. bandWidth := partialPath.amountToReceive for _, reverseEdge := range additionalEdgesWithSrc[bestNode.PubKeyBytes] { processEdge(reverseEdge.sourceNode, reverseEdge.edge, bandWidth, pivot) } } // If the source node isn't found in the next hop map, then a path // doesn't exist, so we terminate in an error. if _, ok := next[sourceVertex]; !ok { return nil, newErrf(ErrNoPathFound, "unable to find a path to "+ "destination") } // Use the nextHop map to unravel the forward path from source to target. pathEdges := make([]*channeldb.ChannelEdgePolicy, 0, len(next)) currentNode := sourceVertex for currentNode != targetVertex { // TODO(roasbeef): assumes no cycles // Determine the next hop forward using the next map. nextNode := next[currentNode] // Add the next hop to the list of path edges. pathEdges = append(pathEdges, nextNode) // Advance current node. currentNode = Vertex(nextNode.Node.PubKeyBytes) } // 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") } return pathEdges, nil } // findPaths implements a k-shortest paths algorithm to find all the reachable // paths between the passed source and target. The algorithm will continue to // traverse the graph until all possible candidate paths have been depleted. // This function implements a modified version of Yen's. To find each path // itself, we utilize our modified version of Dijkstra's found above. When // examining possible spur and root paths, rather than removing edges or // Vertexes from the graph, we instead utilize a Vertex+edge black-list that // will be ignored by our modified Dijkstra's algorithm. With this approach, we // make our inner path finding algorithm aware of our k-shortest paths // algorithm, rather than attempting to use an unmodified path finding // algorithm in a block box manner. func findPaths(tx *bolt.Tx, graph *channeldb.ChannelGraph, source *channeldb.LightningNode, target *btcec.PublicKey, amt lnwire.MilliSatoshi, feeLimit lnwire.MilliSatoshi, numPaths uint32, bandwidthHints map[uint64]lnwire.MilliSatoshi) ([][]*channeldb.ChannelEdgePolicy, error) { ignoredEdges := make(map[uint64]struct{}) ignoredVertexes := make(map[Vertex]struct{}) // TODO(roasbeef): modifying ordering within heap to eliminate final // sorting step? var ( shortestPaths [][]*channeldb.ChannelEdgePolicy candidatePaths pathHeap ) // First we'll find a single shortest path from the source (our // selfNode) to the target destination that's capable of carrying amt // satoshis along the path before fees are calculated. startingPath, err := findPath( tx, graph, nil, source, target, ignoredVertexes, ignoredEdges, amt, feeLimit, bandwidthHints, ) if err != nil { log.Errorf("Unable to find path: %v", err) return nil, err } // Manually insert a "self" edge emanating from ourselves. This // self-edge is required in order for the path finding algorithm to // function properly. firstPath := make([]*channeldb.ChannelEdgePolicy, 0, len(startingPath)+1) firstPath = append(firstPath, &channeldb.ChannelEdgePolicy{ Node: source, }) firstPath = append(firstPath, startingPath...) shortestPaths = append(shortestPaths, firstPath) // While we still have candidate paths to explore we'll keep exploring // the sub-graphs created to find the next k-th shortest path. for k := uint32(1); k < numPaths; k++ { prevShortest := shortestPaths[k-1] // We'll examine each edge in the previous iteration's shortest // path in order to find path deviations from each node in the // path. for i := 0; i < len(prevShortest)-1; i++ { // These two maps will mark the edges and Vertexes // we'll exclude from the next path finding attempt. // These are required to ensure the paths are unique // and loopless. ignoredEdges = make(map[uint64]struct{}) ignoredVertexes = make(map[Vertex]struct{}) // Our spur node is the i-th node in the prior shortest // path, and our root path will be all nodes in the // path leading up to our spurNode. spurNode := prevShortest[i].Node rootPath := prevShortest[:i+1] // Before we kickoff our next path finding iteration, // we'll find all the edges we need to ignore in this // next round. This ensures that we create a new unique // path. for _, path := range shortestPaths { // If our current rootPath is a prefix of this // shortest path, then we'll remove the edge // directly _after_ our spur node from the // graph so we don't repeat paths. if len(path) > i+1 && isSamePath(rootPath, path[:i+1]) { ignoredEdges[path[i+1].ChannelID] = struct{}{} } } // Next we'll remove all entries in the root path that // aren't the current spur node from the graph. This // ensures we don't create a path with loops. for _, hop := range rootPath { node := hop.Node.PubKeyBytes if node == spurNode.PubKeyBytes { continue } ignoredVertexes[Vertex(node)] = struct{}{} } // With the edges that are part of our root path, and // the Vertexes (other than the spur path) within the // root path removed, we'll attempt to find another // shortest path from the spur node to the destination. spurPath, err := findPath( tx, graph, nil, spurNode, target, ignoredVertexes, ignoredEdges, amt, feeLimit, bandwidthHints, ) // If we weren't able to find a path, we'll continue to // the next round. if IsError(err, ErrNoPathFound) { continue } else if err != nil { return nil, err } // Create the new combined path by concatenating the // rootPath to the spurPath. newPathLen := len(rootPath) + len(spurPath) newPath := path{ hops: make([]*channeldb.ChannelEdgePolicy, 0, newPathLen), dist: newPathLen, } newPath.hops = append(newPath.hops, rootPath...) newPath.hops = append(newPath.hops, spurPath...) // TODO(roasbeef): add and consult path finger print // We'll now add this newPath to the heap of candidate // shortest paths. heap.Push(&candidatePaths, newPath) } // If our min-heap of candidate paths is empty, then we can // exit early. if candidatePaths.Len() == 0 { break } // To conclude this latest iteration, we'll take the shortest // path in our set of candidate paths and add it to our // shortestPaths list as the *next* shortest path. nextShortestPath := heap.Pop(&candidatePaths).(path).hops shortestPaths = append(shortestPaths, nextShortestPath) } return shortestPaths, nil }