Feature: Implement constrained k-mer generation and clique search

This commit introduces core functionality for oligonucleotide family tagging, constrained k-mer generation, and clique finding. It also includes updates to the Go language version and refactors the logic for k-mer dissimilarity metrics.
2026-11-09 09:24:41 +00:00 · 2026-11-03 09:25:34 +11:00
1 parent f76e7f03c6
commit 3087c70daa
@@ -0,0 +1,176 @@
+package obigraph
+
+import (
+	"context"
+	"math/rand"
+	"sync"
+)
+
+// NeighborFilter defines an implicit graph over the vertices 0..n-1.
+// It appends to out[:0] the vertices of candidates that are adjacent to v,
+// keeping their order, and returns the resulting slice. It is called
+// concurrently by several workers and must not modify candidates.
+//
+// Describing the adjacency by a filter, instead of a matrix, keeps the memory
+// in O(n) and lets the caller evaluate adjacency in bulk (SIMD, for instance).
+type NeighborFilter func(v int32, candidates, out []int32) []int32
+
+// CliqueOptions tunes FindClique.
+type CliqueOptions struct {
+	// Workers is the number of concurrent searches (default 1).
+	Workers int
+	// Seed seeds the random vertex orders of the restarts.
+	Seed int64
+}
+
+// CliqueResult is the outcome of FindClique.
+type CliqueResult struct {
+	// Clique is the largest clique found (a clique of size >= target if Reached).
+	Clique []int32
+	// Reached is true if len(Clique) >= target.
+	Reached bool
+	// Exhausted is true if the whole search space has been explored. If Reached
+	// is false, it proves that no clique of the target size exists.
+	Exhausted bool
+}
+
+// FindClique looks for a clique of at least target vertices in the graph of n
+// vertices described by filter. It stops as soon as one is found, when the
+// search space is exhausted, or when ctx is done; in the last case, the largest
+// clique met so far is returned.
+//
+// The search is a depth first search with backtracking, pruned when the
+// current clique plus the remaining candidates cannot reach target. The first
+// pass of the first worker follows the natural order of the vertices (greedy
+// "lexicographic" construction); every other pass restarts from a random
+// order, with a work budget that doubles at each restart, so that the search
+// is complete in the long run.
+func FindClique(ctx context.Context, n int, filter NeighborFilter, target int, opts CliqueOptions) CliqueResult {
+	if target <= 0 {
+		return CliqueResult{Reached: true, Exhausted: true}
+	}
+	if n <= 0 {
+		return CliqueResult{Exhausted: true}
+	}
+
+	workers := max(opts.Workers, 1)
+	ctx, cancel := context.WithCancel(ctx)
+	defer cancel()
+
+	var (
+		mutex     sync.Mutex
+		best      []int32
+		exhausted bool
+		wg        sync.WaitGroup
+	)
+
+	publish := func(clique []int32) {
+		mutex.Lock()
+		if len(clique) > len(best) {
+			best = append(best[:0], clique...)
+		}
+		mutex.Unlock()
+	}
+
+	for w := range workers {
+		wg.Go(func() {
+			s := &cliqueSearch{
+				ctx:    ctx,
+				filter: filter,
+				target: target,
+				publish: func(c []int32) {
+					publish(c)
+					if len(c) >= target {
+						cancel()
+					}
+				},
+			}
+			rng := rand.New(rand.NewSource(opts.Seed + int64(w)))
+			candidates := make([]int32, n)
+			for i := range candidates {
+				candidates[i] = int32(i)
+			}
+
+			for restart := 0; ctx.Err() == nil; restart++ {
+				if w > 0 || restart > 0 {
+					rng.Shuffle(n, func(i, j int) { candidates[i], candidates[j] = candidates[j], candidates[i] })
+				}
+				s.budget = int64(n) * int64(target) << min(restart, 20)
+				s.work = 0
+				s.aborted = false
+				s.search(0, candidates)
+
+				if !s.aborted && ctx.Err() == nil {
+					mutex.Lock()
+					exhausted = true
+					mutex.Unlock()
+					cancel()
+				}
+			}
+		})
+	}
+	wg.Wait()
+
+	return CliqueResult{
+		Clique:    best,
+		Reached:   len(best) >= target,
+		Exhausted: exhausted,
+	}
+}
+
+type cliqueSearch struct {
+	ctx     context.Context
+	filter  NeighborFilter
+	target  int
+	publish func([]int32)
+
+	current []int32   // the clique under construction
+	buffers [][]int32 // candidate list of each depth
+	bestLen int
+
+	budget  int64 // maximum work (number of candidates tested) for this restart
+	work    int64
+	aborted bool // budget or context exhausted before the end of the exploration
+}
+
+func (s *cliqueSearch) search(depth int, candidates []int32) {
+	for i := range candidates {
+		if depth+len(candidates)-i < s.target {
+			return
+		}
+		if s.work > s.budget || s.ctx.Err() != nil {
+			s.aborted = true
+			return
+		}
+
+		v := candidates[i]
+		s.current = append(s.current[:depth], v)
+		if len(s.current) > s.bestLen {
+			s.bestLen = len(s.current)
+			s.publish(s.current)
+			if s.bestLen >= s.target {
+				s.aborted = true // the search is over: do not report an exhaustion
+				return
+			}
+		}
+
+		rest := candidates[i+1:]
+		if depth+1+len(rest) < s.target {
+			continue
+		}
+		for len(s.buffers) <= depth+1 {
+			s.buffers = append(s.buffers, nil)
+		}
+		next := s.filter(v, rest, s.buffers[depth+1][:0])
+		s.buffers[depth+1] = next
+		s.work += int64(len(rest))
+
+		if depth+1+len(next) < s.target {
+			continue
+		}
+		s.search(depth+1, next)
+		if s.aborted {
+			return
+		}
+	}
+}
@@ -0,0 +1,143 @@
+package obigraph
+
+import (
+	"context"
+	"math/bits"
+	"math/rand"
+	"testing"
+	"time"
+)
+
+// adjacency matrix filter for small graphs
+func matrixFilter(adj [][]bool) NeighborFilter {
+	return func(v int32, candidates, out []int32) []int32 {
+		for _, c := range candidates {
+			if adj[v][c] {
+				out = append(out, c)
+			}
+		}
+		return out
+	}
+}
+
+func randomGraph(rng *rand.Rand, n int, p float64) [][]bool {
+	adj := make([][]bool, n)
+	for i := range adj {
+		adj[i] = make([]bool, n)
+	}
+	for i := 0; i < n; i++ {
+		for j := i + 1; j < n; j++ {
+			if rng.Float64() < p {
+				adj[i][j], adj[j][i] = true, true
+			}
+		}
+	}
+	return adj
+}
+
+// maximum clique size by brute force over all the subsets (n <= 20)
+func bruteMaxClique(adj [][]bool) int {
+	n := len(adj)
+	best := 0
+	for mask := 1; mask < 1<<n; mask++ {
+		size := bits.OnesCount(uint(mask))
+		if size <= best {
+			continue
+		}
+		ok := true
+		for i := 0; i < n && ok; i++ {
+			if mask>>i&1 == 0 {
+				continue
+			}
+			for j := i + 1; j < n; j++ {
+				if mask>>j&1 == 1 && !adj[i][j] {
+					ok = false
+					break
+				}
+			}
+		}
+		if ok {
+			best = size
+		}
+	}
+	return best
+}
+
+func isClique(adj [][]bool, c []int32) bool {
+	seen := map[int32]bool{}
+	for i, a := range c {
+		if seen[a] {
+			return false
+		}
+		seen[a] = true
+		for _, b := range c[i+1:] {
+			if !adj[a][b] {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+func TestFindCliqueAgainstBruteForce(t *testing.T) {
+	rng := rand.New(rand.NewSource(1))
+	for trial := 0; trial < 40; trial++ {
+		n := 8 + rng.Intn(10)
+		adj := randomGraph(rng, n, 0.3+0.5*rng.Float64())
+		maxSize := bruteMaxClique(adj)
+		filter := matrixFilter(adj)
+
+		for _, workers := range []int{1, 3} {
+			r := FindClique(context.Background(), n, filter, maxSize, CliqueOptions{Workers: workers})
+			if !r.Reached || len(r.Clique) < maxSize || !isClique(adj, r.Clique) {
+				t.Fatalf("trial %d: target %d not reached: %+v", trial, maxSize, r)
+			}
+
+			r = FindClique(context.Background(), n, filter, maxSize+1, CliqueOptions{Workers: workers})
+			if r.Reached || !r.Exhausted {
+				t.Fatalf("trial %d: size %d cannot exist, got %+v", trial, maxSize+1, r)
+			}
+			// best effort: a valid clique, not necessarily a maximum one
+			if len(r.Clique) < 1 || len(r.Clique) > maxSize || !isClique(adj, r.Clique) {
+				t.Fatalf("trial %d: invalid best clique %v (maximum is %d)", trial, r.Clique, maxSize)
+			}
+		}
+	}
+}
+
+func TestFindCliqueTrivialTargets(t *testing.T) {
+	adj := randomGraph(rand.New(rand.NewSource(2)), 5, 0.5)
+	if r := FindClique(context.Background(), 5, matrixFilter(adj), 0, CliqueOptions{}); !r.Reached {
+		t.Fatal("target 0 is always reached")
+	}
+	if r := FindClique(context.Background(), 0, matrixFilter(adj), 1, CliqueOptions{}); r.Reached {
+		t.Fatal("no clique in an empty graph")
+	}
+	if r := FindClique(context.Background(), 5, matrixFilter(adj), 1, CliqueOptions{}); !r.Reached || len(r.Clique) != 1 {
+		t.Fatalf("a single vertex is a clique: %+v", r)
+	}
+}
+
+// A hopeless search must stop with the deadline and return a valid clique.
+// (When the target is far above the clique number of a sparse graph, pruning
+// proves the absence at once: see TestFindCliqueAgainstBruteForce.)
+func TestFindCliqueTimeout(t *testing.T) {
+	// dense graph: its largest clique is far below the target, but pruning only
+	// bites after many levels, so the search cannot finish within the deadline
+	const n = 300
+	adj := randomGraph(rand.New(rand.NewSource(3)), n, 0.9)
+	ctx, cancel := context.WithTimeout(context.Background(), 300*time.Millisecond)
+	defer cancel()
+
+	start := time.Now()
+	r := FindClique(ctx, n, matrixFilter(adj), 150, CliqueOptions{Workers: 2})
+	if elapsed := time.Since(start); elapsed > 3*time.Second {
+		t.Fatalf("deadline not honoured: %v", elapsed)
+	}
+	if r.Reached || r.Exhausted {
+		t.Fatalf("size 150 cannot be reached nor proven absent in time: %+v", r)
+	}
+	if len(r.Clique) < 2 || !isClique(adj, r.Clique) {
+		t.Fatalf("invalid best clique %v", r.Clique)
+	}
+}