prysm-pulse/shared/aggregation/maxcover.go
Victor Farazdagi a019a0db4c
Combines func params of the same type (#7500)
* combines func params

* update leftovers

Co-authored-by: prylabs-bulldozer[bot] <58059840+prylabs-bulldozer[bot]@users.noreply.github.com>
2020-10-12 15:43:19 +00:00

204 lines
6.3 KiB
Go

package aggregation
import (
"fmt"
"sort"
"github.com/pkg/errors"
"github.com/prysmaticlabs/go-bitfield"
)
// ErrInvalidMaxCoverProblem is returned when Maximum Coverage problem was initialized incorrectly.
var ErrInvalidMaxCoverProblem = errors.New("invalid max_cover problem")
// MaxCoverProblem defines Maximum Coverage problem.
//
// Problem is defined as MaxCover(U, S, k): S', where:
// U is a finite set of objects, where |U| = n. Furthermore, let S = {S_1, ..., S_m} be all
// subsets of U, that's their union is equal to U. Then, Maximum Coverage is the problem of
// finding such a collection S' of subsets from S, where |S'| <= k, and union of all subsets in S'
// covering U with maximum cardinality.
//
// The current implementation captures the original MaxCover problem, and the variant where
// additional invariant is enforced: all elements of S' must be disjoint. This comes handy when
// we need to aggregate bitsets, and overlaps are not allowed.
//
// For more details, see:
// "Analysis of the Greedy Approach in Problems of Maximum k-Coverage" by Hochbaum and Pathria.
// https://hochbaum.ieor.berkeley.edu/html/pub/HPathria-max-k-coverage-greedy.pdf
type MaxCoverProblem struct {
Candidates MaxCoverCandidates
}
// MaxCoverCandidate represents a candidate set to be used in aggregation.
type MaxCoverCandidate struct {
key int
bits *bitfield.Bitlist
score uint64
processed bool
}
// MaxCoverCandidates is defined to allow group operations (filtering, sorting) on all candidates.
type MaxCoverCandidates []*MaxCoverCandidate
// NewMaxCoverCandidate returns initialized candidate.
func NewMaxCoverCandidate(key int, bits *bitfield.Bitlist) *MaxCoverCandidate {
return &MaxCoverCandidate{
key: key,
bits: bits,
}
}
// Cover calculates solution to Maximum k-Cover problem in O(knm), where
// n is number of candidates and m is a length of bitlist in each candidate.
func (mc *MaxCoverProblem) Cover(k int, allowOverlaps, allowDuplicates bool) (*Aggregation, error) {
if len(mc.Candidates) == 0 {
return nil, errors.Wrap(ErrInvalidMaxCoverProblem, "cannot calculate set coverage")
}
if len(mc.Candidates) < k {
k = len(mc.Candidates)
}
if err := mc.Candidates.validate(); err != nil {
return nil, err
}
if !allowDuplicates {
mc.Candidates.dedup(allowOverlaps)
}
solution := &Aggregation{
Coverage: bitfield.NewBitlist(mc.Candidates[0].bits.Len()),
Keys: make([]int, 0, k),
}
remainingBits := mc.Candidates.union()
if remainingBits == nil {
return nil, errors.Wrap(ErrInvalidMaxCoverProblem, "empty bitlists")
}
for len(solution.Keys) < k && len(mc.Candidates) > 0 {
// Score candidates against remaining bits.
// Filter out processed and overlapping (when disallowed).
// Sort by score in a descending order.
mc.Candidates.score(remainingBits).filter(solution.Coverage, allowOverlaps).sort()
for _, candidate := range mc.Candidates {
if len(solution.Keys) >= k {
break
}
if !candidate.processed {
if !allowOverlaps && solution.Coverage.Overlaps(*candidate.bits) {
// Overlapping candidates violate non-intersection invariant.
candidate.processed = true
continue
}
solution.Coverage = solution.Coverage.Or(*candidate.bits)
solution.Keys = append(solution.Keys, candidate.key)
remainingBits = remainingBits.And(candidate.bits.Not())
candidate.processed = true
break
}
}
}
return solution, nil
}
// score updates scores of candidates, taking into account the uncovered elements only.
func (cl *MaxCoverCandidates) score(uncovered bitfield.Bitlist) *MaxCoverCandidates {
for i := 0; i < len(*cl); i++ {
(*cl)[i].score = (*cl)[i].bits.And(uncovered).Count()
}
return cl
}
// filter removes processed, overlapping and zero-score candidates.
func (cl *MaxCoverCandidates) filter(covered bitfield.Bitlist, allowOverlaps bool) *MaxCoverCandidates {
overlaps := func(e bitfield.Bitlist) bool {
return !allowOverlaps && covered.Len() == e.Len() && covered.Overlaps(e)
}
cur, end := 0, len(*cl)
for cur < end {
e := *(*cl)[cur]
if e.processed || overlaps(*e.bits) || e.score == 0 {
(*cl)[cur] = (*cl)[end-1]
end--
continue
}
cur++
}
*cl = (*cl)[:end]
return cl
}
// sort orders candidates by their score, starting from the candidate with the highest score.
func (cl *MaxCoverCandidates) sort() *MaxCoverCandidates {
sort.Slice(*cl, func(i, j int) bool {
if (*cl)[i].score == (*cl)[j].score {
return (*cl)[i].key < (*cl)[j].key
}
return (*cl)[i].score > (*cl)[j].score
})
return cl
}
// union merges all candidate bitlists using logical OR operator.
func (cl *MaxCoverCandidates) union() bitfield.Bitlist {
if len(*cl) == 0 {
return nil
}
if (*cl)[0].bits == nil || (*cl)[0].bits.Len() == 0 {
return nil
}
ret := bitfield.NewBitlist((*cl)[0].bits.Len())
for i := 0; i < len(*cl); i++ {
if *(*cl)[i].bits != nil {
ret = ret.Or(*(*cl)[i].bits)
}
}
return ret
}
// dedup removes duplicate candidates (ones with the same bits set on).
func (cl *MaxCoverCandidates) dedup(allowOverlaps bool) *MaxCoverCandidates {
if len(*cl) < 2 {
return cl
}
uncoveredBits := cl.union()
if uncoveredBits == nil {
return cl
}
cl.score(uncoveredBits).sort()
for i := 1; i < len(*cl); i++ {
nonOverlappingBits := (*cl)[i-1].bits.Xor(*(*cl)[i].bits)
if (*cl)[i-1].score == (*cl)[i].score && nonOverlappingBits.Count() == 0 {
(*cl)[i-1].processed = true
}
}
return cl.filter(bitfield.NewBitlist((*cl)[0].bits.Len()), allowOverlaps)
}
// validate checks candidates for validity (equal bitlength etc).
func (cl *MaxCoverCandidates) validate() error {
if len(*cl) == 0 {
return errors.Wrap(ErrInvalidMaxCoverProblem, "empty list of candidates")
}
if (*cl)[0].bits == nil || (*cl)[0].bits.Len() == 0 {
return errors.Wrap(ErrInvalidMaxCoverProblem, "bitlist cannot be nil or empty")
}
bitlistLen := (*cl)[0].bits.Len()
for i := 1; i < len(*cl); i++ {
if (*cl)[i].bits == nil || (*cl)[i].bits.Len() == 0 {
return errors.Wrap(ErrInvalidMaxCoverProblem, "bitlist cannot be nil or empty")
}
if bitlistLen != (*cl)[i].bits.Len() {
return errors.Wrap(ErrInvalidMaxCoverProblem, "bitlists of different length")
}
}
return nil
}
// String provides string representation of a candidate.
func (c *MaxCoverCandidate) String() string {
return fmt.Sprintf("{%v, %#b, s%d, %t}", c.key, c.bits, c.score, c.processed)
}