+ // 1. Select k (of |D|, whichever is smaller) arbitrary events e_1, ..., e_k from D
+ const auto D_hat = [&]() {
+ const size_t size = std::min(k, D.size());
+ std::vector<const UnfoldingEvent*> D_hat(size);
+ // TODO: Since any subset suffices for computing `k`-partial alternatives,
+ // potentially select intelligently here (e.g. perhaps pick events
+ // with transitions that we know are totally independent). This may be
+ // especially important if the enumeration is the slowest part of
+ // UDPOR
+ //
+ // For now, simply pick the first `k` events
+ std::copy_n(D.begin(), size, D_hat.begin());
+ return D_hat;
+ }();
+
+ // 2. Build a U-comb <s_1, ..., s_k> of size k, where spike `s_i` contains
+ // all events in conflict with `e_i`
+ //
+ // 3. EXCEPT those events e' for which [e'] + C is not a configuration or
+ // [e'] intersects D
+ //
+ // NOTE: This is an expensive operation as we must traverse the entire unfolding
+ // and compute `C.is_compatible_with(History)` for every event in the structure :/.
+ // A later performance improvement would be to incorporate the work of Nguyen et al.
+ // into SimGrid which associated additonal data structures with each unfolding event.
+ // Since that is a rather complicated addition, we defer it to a later time...
+ Comb comb(k);
+
+ for (const auto* e : U) {
+ for (unsigned i = 0; i < k; i++) {
+ const UnfoldingEvent* e_i = D_hat[i];
+ if (const auto e_local_config = History(e);
+ e_i->conflicts_with(e) and (not D.intersects(e_local_config)) and is_compatible_with(e_local_config)) {
+ comb[i].push_back(e);
+ }
+ }
+ }
+
+ // 4. Find any such combination <e_1', ..., e_k'> in comb satisfying
+ // ~(e_i' # e_j') for i != j
+ //
+ // NOTE: This is a VERY expensive operation: it enumerates all possible
+ // ways to select an element from each spike. Unfortunately there's no
+ // way around the enumeration, as computing a full alternative in general is
+ // NP-complete (although computing the k-partial alternative is polynomial in
+ // the number of events)
+ const auto map_events = [](const std::vector<Spike::const_iterator>& spikes) {
+ std::vector<const UnfoldingEvent*> events;
+ for (const auto& event_in_spike : spikes) {
+ events.push_back(*event_in_spike);
+ }
+ return EventSet(std::move(events));
+ };
+ const auto alternative =
+ std::find_if(comb.combinations_begin(), comb.combinations_end(),
+ [&map_events](const auto& vector) { return map_events(vector).is_conflict_free(); });
+
+ // No such alternative exists
+ if (alternative == comb.combinations_end()) {
+ return std::nullopt;
+ }
+
+ // 5. J := [e_1] + [e_2] + ... + [e_k] is a k-partial alternative
+ return Configuration(History(map_events(*alternative)));