autopilot/prefattach+interface: add API NodeScores

This commit adds a new method NodeScores to the AttachementHeuristic
interface. Its intended use is to score a set of nodes according to
their preference as channel counterparties.

The PrefAttach heuristic gets a NodeScores method that will score the
ndoes according to their number of already existing channels, similar to
what is done already in Select.

autopilot/prefattach.go

@@ -4,6 +4,7 @@ import (
 	"bytes"
 	"fmt"
 	prand "math/rand"
+	"net"
 	"time"
 
 	"github.com/btcsuite/btcd/btcec"
@@ -249,3 +250,108 @@ func (p *ConstrainedPrefAttachment) Select(self *btcec.PublicKey, g ChannelGraph
 		return nil, fmt.Errorf("err")
 	}
 }
+
+// NodeScores is a method that given the current channel graph, current set of
+// local channels and funds available, scores the given nodes according the the
+// preference of opening a channel with them.
+//
+// The heuristic employed by this method is one that attempts to promote a
+// scale-free network globally, via local attachment preferences for new nodes
+// joining the network with an amount of available funds to be allocated to
+// channels. Specifically, we consider the degree of each node (and the flow
+// in/out of the node available via its open channels) and utilize the
+// Barabási–Albert model to drive our recommended attachment heuristics. If
+// implemented globally for each new participant, this results in a channel
+// graph that is scale-free and follows a power law distribution with k=-3.
+//
+// The returned scores will be in the range [0.0, 1.0], where higher scores are
+// given to nodes already having high connectivity in the graph.
+//
+// NOTE: This is a part of the AttachmentHeuristic interface.
+func (p *ConstrainedPrefAttachment) NodeScores(g ChannelGraph, chans []Channel,
+	fundsAvailable btcutil.Amount, nodes map[NodeID]struct{}) (
+	map[NodeID]*AttachmentDirective, error) {
+
+	// Count the number of channels in the graph. We'll also count the
+	// number of channels as we go for the nodes we are interested in, and
+	// record their addresses found in the db.
+	var graphChans int
+	nodeChanNum := make(map[NodeID]int)
+	addresses := make(map[NodeID][]net.Addr)
+	if err := g.ForEachNode(func(n Node) error {
+		var nodeChans int
+		err := n.ForEachChannel(func(_ ChannelEdge) error {
+			nodeChans++
+			graphChans++
+			return nil
+		})
+		if err != nil {
+			return err
+		}
+
+		// If this node is not among our nodes to score, we can return
+		// early.
+		nID := NodeID(n.PubKey())
+		if _, ok := nodes[nID]; !ok {
+			return nil
+		}
+
+		// Otherwise we'll record the number of channels, and also
+		// populate the address in our channel candidates map.
+		nodeChanNum[nID] = nodeChans
+		addresses[nID] = n.Addrs()
+
+		return nil
+	}); err != nil {
+		return nil, err
+	}
+
+	// If there are no channels in the graph we cannot determine any
+	// preferences, so we return, indicating all candidates get a score of
+	// zero.
+	if graphChans == 0 {
+		return nil, nil
+	}
+
+	existingPeers := make(map[NodeID]struct{})
+	for _, c := range chans {
+		existingPeers[c.Node] = struct{}{}
+	}
+
+	// For each node in the set of nodes, count their fraction of channels
+	// in the graph, and use that as the score.
+	candidates := make(map[NodeID]*AttachmentDirective)
+	for nID, nodeChans := range nodeChanNum {
+		// As channel size we'll use the maximum channel size available.
+		chanSize := p.constraints.MaxChanSize
+		if fundsAvailable-chanSize < 0 {
+			chanSize = fundsAvailable
+		}
+
+		_, ok := existingPeers[nID]
+
+		switch {
+
+		// If the node is among or existing channel peers, we don't
+		// need another channel.
+		case ok:
+			continue
+
+		// If the amount is too small, we don't want to attempt opening
+		// another channel.
+		case chanSize == 0 || chanSize < p.constraints.MinChanSize:
+			continue
+		}
+
+		// Otherwise we score the node according to its fraction of
+		// channels in the graph.
+		score := float64(nodeChans) / float64(graphChans)
+		candidates[nID] = &AttachmentDirective{
+			NodeID:  nID,
+			ChanAmt: chanSize,
+			Score:   score,
+		}
+	}
+
+	return candidates, nil
+}