From 3591c58f6d9cc44aad31683f1282e1bcb9c86451 Mon Sep 17 00:00:00 2001 From: stefiosif Date: Fri, 10 Feb 2023 18:26:48 +0200 Subject: [PATCH] Improve readability --- include/algorithm/breadth_first_search.h | 2 +- include/algorithm/frigioni.h | 235 +++++++++++++---------- include/algorithm/italiano.h | 71 +++---- include/algorithm/roditty_zwick.h | 27 +-- include/algorithm/tarjan.h | 24 +-- include/graph/breadth_first_tree.h | 16 +- 6 files changed, 217 insertions(+), 158 deletions(-) diff --git a/include/algorithm/breadth_first_search.h b/include/algorithm/breadth_first_search.h index 6309283..c82441d 100644 --- a/include/algorithm/breadth_first_search.h +++ b/include/algorithm/breadth_first_search.h @@ -14,7 +14,7 @@ class BreadthFirstSearch { public: BreadthFirstSearch() = default; - BreadthFirstSearch(std::unordered_map> adjList) + explicit BreadthFirstSearch(std::unordered_map> adjList) : adjList(adjList) {} // Traverse whole graph using the BFS search, and save the tree graph diff --git a/include/algorithm/frigioni.h b/include/algorithm/frigioni.h index 933c42e..90e4c49 100644 --- a/include/algorithm/frigioni.h +++ b/include/algorithm/frigioni.h @@ -29,7 +29,7 @@ private: std::unordered_map> TC; // For each SCC, store a reachability tree created as a BFS tree - std::unordered_map> RT; + std::unordered_map, BreadthFirstTree, HashSCC> RT; // For each SCC, store collections of incoming, outgoing and internal edges struct Edges { @@ -37,37 +37,50 @@ private: std::set> inc; std::set> out; }; - std::unordered_map E; - + std::unordered_map, Edges, HashSCC> E; + + // Structure that keeps candidate components to use as a hook + std::unordered_map, std::stack, HashSCC> H; + // Decremental maintenance of strongly connected components RodittyZwick rodittyZwick; + + // Delete internal edge e(u, v) + void removeInternal(const T& u, const T& v); + + // Delete external edge e(u, v) + void removeExternal(const T& u, const T& v); + + // Repair reachability trees + void repairTrees(); + + // + void splitEdges(std::unordered_map>& L, std::unordered_map> C, const T& w); }; template void Frigioni::init() { - auto SCCs = Tarjan(this->G.adjList).execute(); rodittyZwick = RodittyZwick(this->G); rodittyZwick.init(); + auto C = rodittyZwick.getComponentMap(); - for (auto& scc : SCCs) { - RT[scc.id] = BreadthFirstTree(this->G, scc.id); + for (const auto& w : std::views::keys(C)) { + RT[C[w]] = BreadthFirstTree(this->G, w); for (const auto& u : this->G.vertices()) { for (const auto& v : this->G.adjList[u]) { - if (scc.member(u)) { - if (scc.member(v)) - E[scc.id].in.insert(std::make_pair(u, v)); - else - E[scc.id].out.insert(std::make_pair(u, v)); - } else if (scc.member(v)) { - E[scc.id].inc.insert(std::make_pair(u, v)); - } + if (!C[w].contains(u) && C[w].contains(v)) + E[C[w]].inc.insert({ u, v }); + else if (C[w].contains(u) && !C[w].contains(v)) + E[C[w]].out.insert({ u, v }); + else + E[C[w]].in.insert({ u, v }); TC[u][v] = false; } } } - for (auto& scc : SCCs) { - for (const auto& u : scc.vertices()) { - for (const auto& v : RT[scc.id].vertices()) { + for (const auto& w : std::views::keys(C)) { + for (const auto& u : C[w].vertices()) { + for (const auto& v : RT[C[w]].vertices()) { TC[u][v] = true; } } @@ -85,104 +98,132 @@ void Frigioni::remove(const std::vector>& edges) { std::vector> Eext; for (const auto& [u, v] : edges) { + if (!this->G.adjList[u].contains(v)) continue; + if (rodittyZwick.query(u, v)) Eint.push_back({ u, v }); else Eext.push_back({ u, v }); } + for (const auto& [u, v] : Eint) removeInternal(u, v); + for (const auto& [u, v] : Eext) removeExternal(u, v); - std::unordered_map> H; - for (const auto& [u, v] : Eint) { - this->G.remove(u, v); - rodittyZwick.remove(u, v); + repairTrees(); +} - if (!rodittyZwick.query(u, v)) { - TC[u][v] = false; - auto C = rodittyZwick.getSCCs(); +template +void Frigioni::removeInternal(const T& u, const T& v) { + this->G.remove(u, v); + auto L = rodittyZwick.getComponentMap(); + rodittyZwick.remove(u, v); + auto C = rodittyZwick.getComponentMap(); - E[C[u].id].inc.erase({ u, v }); - E[C[u].id].out.erase({ u, v }); - E[C[u].id].in.erase({ u, v }); - auto D = E[C[u].id]; - E.erase(C[u].id); - - for (const auto& id : std::views::keys(C)) { - if (RT[id].contains(id, v)) { - if (E[C[v].id].inc.size() > 1) - H[id].push(C[v].id); - else { - for (const auto& w : C[id].vertices()) - TC[w][v] = false; - for (const auto& c : E[v].out) - H[id].push(C[c.second].id); - } - RT[id].adjList[u].erase(v); - } - } - - for (const auto& [w, z] : D.inc) { - E[C[z].id].inc.insert({ w, z }); - } - - for (const auto& [w, z] : D.out) { - E[C[w].id].out.insert({ w, z }); - } - - for (const auto& [w, z] : D.in) { - if (C[w] == C[z]) - E[C[w].id].in.insert({ w, z }); - else { - E[C[w].id].out.insert({ w, z }); - E[C[z].id].in.insert({ w, z }); - } - } - } else { - E[u].in.erase({ u, v }); - } + if (rodittyZwick.query(u, v)) { + E[C[u]].in.erase({ u, v }); + return; } - for (const auto& [u, v] : Eext) { - this->G.remove(u, v); - auto C = rodittyZwick.getSCCs(); - - for (const auto& id : std::views::keys(C)) { - if (RT[id].contains(id, v)) { - if (E[C[v].id].inc.size() > 1) - H[id].push(C[v].id); - else { - for (const auto& w : C[id].vertices()) - TC[w][v] = false; - for (const auto& c : E[v].out) - H[id].push(C[c.second].id); - } - RT[id].adjList[u].erase(v); - } - } + if (L[u] == C[u]) { + E[L[u]].out.erase({ u, v }); + E.erase(L[v]); + splitEdges(L, C, v); + } + else { + E[L[v]].inc.erase({ u, v }); + E.erase(L[u]); + splitEdges(L, C, u); } - auto C = rodittyZwick.getSCCs(); - for (const auto& id : std::views::keys(rodittyZwick.getSCCs())) { - while (H[id].size() > 0) { - const auto& h = H[id].top(); - bool found = false; - - for (const auto& [u, v] : E[h].inc) { - if (RT[id].contains(id, u)) { - RT[id].adjList[u].insert(h); - found = true; + for (const auto& w : std::views::keys(C)) { + if (!RT[C[w]].contains(v)) continue; + + RT[C[w]].removeEdgeTo(v); + if (E[C[v]].inc.size() > 0) { + H[C[w]].push(v); /*h mipos C[v].id?*/ + continue; + } + for (const auto& x : C[w].vertices()) { + for (const auto& y : C[v].vertices()) { + TC[x][y] = false; + } + } + for (const auto& [a, b] : E[C[v]].out) + H[C[w]].push(b); + } +} + +template +void Frigioni::removeExternal(const T& u, const T& v) { + this->G.remove(u, v); + auto C = rodittyZwick.getComponentMap(); + E[C[v]].inc.erase({ u, v }); + E[C[u]].out.erase({ u, v }); + + for (const auto& w : std::views::keys(C)) { + if (!RT[C[w]].contains(v)) continue; + + RT[C[w]].removeEdgeTo(v); + if (E[C[v]].inc.size() > 0) { + H[C[w]].push(v); + continue; + } + for (const auto& x : C[w].vertices()) { + for (const auto& y : C[v].vertices()) { + TC[x][y] = false; + } + } + for (const auto& [a, b] : E[C[v]].out) + H[C[w]].push(b); + } +} + +template +void Frigioni::repairTrees() { + auto C = rodittyZwick.getComponentMap(); + for (const auto& w : std::views::keys(C)) { + while (H[C[w]].size() > 0) { + const auto& h = H[C[w]].top(); + H[C[w]].pop(); + bool foundHook = false; + + for (const auto& [a, b] : E[C[h]].inc) { + if (RT[C[w]].adjList[w].contains(a)) { + RT[C[w]].insert(a, h); + foundHook = true; break; } } - H[id].pop(); - if (!found) { - auto C = rodittyZwick.getSCCs(); - for (const auto& w : C[id].vertices()) - TC[w][h] = false; + if (foundHook) continue; - for (const auto& [u, v] : E[h].out) { - H[id].push(v); + for (const auto& x : C[w].vertices()) { + for (const auto& y : C[h].vertices()) { + TC[x][y] = false; } } + for (const auto& [a, b] : E[C[h]].out) { + if (RT[C[w]].adjList[h].contains(a)) { + H[C[w]].push(b); + } + } + } + } +} + +template +void Frigioni::splitEdges(std::unordered_map>& L, std::unordered_map> C, const T& w) { + for (const auto& [a, b] : E[L[w]].inc) + E[C[b]].inc.insert({ a, b }); + + for (const auto& [a, b] : E[L[w]].out) + E[C[a]].out.insert({ a, b }); + + for (const auto& [a, b] : E[L[w]].in) { + if (C[a] == C[b]) { + E[C[a]].in.insert({ a, b }); + } + else { + E[C[a]].out.insert({ a, b }); + E[C[b]].in.insert({ a, b }); } } } diff --git a/include/algorithm/italiano.h b/include/algorithm/italiano.h index ad6083d..af78723 100644 --- a/include/algorithm/italiano.h +++ b/include/algorithm/italiano.h @@ -3,7 +3,6 @@ #include "algorithm/decremental_reachability.h" #include "graph/breadth_first_tree.h" - #include namespace algo { @@ -25,7 +24,7 @@ public: // Delete collection of edges void remove(const std::vector>& edges) override; - // Delete edge e(u, v) and explicitely maintain the transitive closure + // Delete edge e(u, v) and explicitly maintain the transitive closure void remove(const T& u, const T& v); private: // Transitive closure matrix @@ -41,8 +40,11 @@ private: }; std::unordered_map E; + // + std::unordered_map> H; + // Repair reachability trees after edge deletions - void repairTrees(std::unordered_map>& H); + void repairTrees(); }; template @@ -67,53 +69,54 @@ bool Italiano::query(const T& u, const T& v) { template void Italiano::remove(const std::vector>& edges) { - for (const auto& [u, v] : edges) + for (const auto& [u, v] : edges) { + if (!this->G.adjList[u].contains(v)) continue; remove(u, v); + } } template void Italiano::remove(const T& u, const T& v) { - if (!this->G.adjList[u].contains(v)) return; - - std::unordered_map> H; - for (const auto& w : this->G.vertices()) { - if (RT[w].contains(u, v)) { - if (E[v].inc.size() > 1) - H[w].push(v); - else { - TC[w][v] = false; - for (const auto& c : E[v].out) - H[w].push(c); - } - RT[w].adjList[u].erase(v); - } - } + this->G.remove(u, v); E[u].out.erase(v); E[v].inc.erase(u); - this->G.remove(u, v); + + for (const auto& w : this->G.vertices()) { + if (!RT[w].adjList[u].contains(v)) continue; - repairTrees(H); + RT[w].adjList[u].erase(v); + if (E[v].inc.size() > 0) { + H[w].push(v); + continue; + } + TC[w][v] = false; + for (const auto& c : E[v].out) + H[w].push(c); + } + repairTrees(); } template -void Italiano::repairTrees(std::unordered_map>& H) { - for (const auto& z : this->G.vertices()) { - while (H[z].size() > 0) { - const auto& h = H[z].top(); - bool found = false; +void Italiano::repairTrees() { + for (const auto& w : this->G.vertices()) { + while (H[w].size() > 0) { + const auto& h = H[w].top(); + H[w].pop(); + bool foundHook = false; for (const auto& i : E[h].inc) { - if (RT[z].contains(z, i)) { - RT[z].adjList[i].insert(h); - found = true; + if (RT[w].adjList[w].contains(i)) { + RT[w].adjList[i].insert(h); + foundHook = true; break; } } - H[z].pop(); - if (!found) { - TC[z][h] = false; - for (const auto& o : E[h].out) { - H[z].push(o); + if (foundHook) continue; + + TC[w][h] = false; + for (const auto& o : E[h].out) { + if (RT[w].adjList[h].contains(o)) { + H[w].push(o); } } } diff --git a/include/algorithm/roditty_zwick.h b/include/algorithm/roditty_zwick.h index fb00aef..4b83c2c 100644 --- a/include/algorithm/roditty_zwick.h +++ b/include/algorithm/roditty_zwick.h @@ -29,7 +29,7 @@ public: // Remove edge (u,v) and update A accordingly for fast checking query void remove(const T& u, const T& v); - std::unordered_map> getSCCs() { return C; } + std::unordered_map> getComponentMap() { return C; } private: // Array used to answer strong connectivity queries in O(1) time std::unordered_map A; @@ -51,16 +51,16 @@ template void RodittyZwick::findSCC(graph::Digraph G) { auto SCCs = Tarjan(G.adjList).execute(); - for (auto& SCC : SCCs) { - const auto& w = SCC.id; + for (auto& c : SCCs) { + const auto& w = c.id; - for (const auto& v : SCC.vertices()) + for (const auto& v : c.vertices()) A[v] = w; - Out[w] = BreadthFirstTree(SCC, w); - In[w] = BreadthFirstTree(SCC.reverse(), w); + Out[w] = BreadthFirstTree(c, w); + In[w] = BreadthFirstTree(c.reverse(), w); - C[w] = SCC; + C[w] = c; } } @@ -82,19 +82,20 @@ void RodittyZwick::remove(const T& u, const T& v) { this->G.remove(u, v); // If u and v are not in the same SCC, do nothing - if (A[u] != A[v]) return; + if (A[u] != A[v]) + return; - // If edge (u,v) is not contained in both inTree and outTree do nothing - if (!In[w].adjList[u].contains(v) && - !Out[w].adjList[u].contains(v)) + // If edge (u,v) is not contained in both inTree and outTree do nothing TODO:remove useless comments + // is this not better if i utilize A matrix, since we are going traversing between components.. ? TODO + if (!In[w].adjList[u].contains(v) && !Out[w].adjList[u].contains(v)) return; // Update In(w) and Out(w) Out[w] = BreadthFirstTree(C[w], w); In[w] = BreadthFirstTree(C[w].reverse(), w); - // If a SCC is broken, compute all SCCs again - if (!In[w].adjList.count(u) || !Out[w].adjList.count(v)) + // If a SCC is broken, compute the new SCCs + if (!In[w].contains(u) || !Out[w].contains(v)) findSCC(C[w]); } diff --git a/include/algorithm/tarjan.h b/include/algorithm/tarjan.h index 9501548..a3452bb 100644 --- a/include/algorithm/tarjan.h +++ b/include/algorithm/tarjan.h @@ -18,7 +18,7 @@ public: // auto execute(); - + // void strongConnect(const T& u); private: @@ -26,33 +26,33 @@ private: std::stack S; std::int16_t index = 0; std::vector> SCCs; - T cid; + T cid{}; struct Vertex { int index = -1; int lowlink = -1; bool onStack = false; }; - std::unordered_map vmap; + std::unordered_map V; }; template void Tarjan::strongConnect(const T& u) { - vmap[u].index = vmap[u].lowlink = index++; + V[u].index = V[u].lowlink = index++; S.push(u); - vmap[u].onStack = true; + V[u].onStack = true; for (const auto& w : adjList[u]) { - if (vmap[w].index == -1) { + if (V[w].index == -1) { strongConnect(w); - vmap[u].lowlink = std::min(vmap[u].lowlink, vmap[w].lowlink); - } else if (vmap[w].onStack) { - vmap[u].lowlink = std::min(vmap[u].lowlink, vmap[w].index); + V[u].lowlink = std::min(V[u].lowlink, V[w].lowlink); + } else if (V[w].onStack) { + V[u].lowlink = std::min(V[u].lowlink, V[w].index); } } // If u is a root node, pop the stack and generate an SCC - if (vmap[u].lowlink == vmap[u].index) { + if (V[u].lowlink == V[u].index) { std::unordered_map> scc; bool finished = false; cid = S.top(); @@ -60,7 +60,7 @@ void Tarjan::strongConnect(const T& u) { do { const auto w = S.top(); S.pop(); - vmap[w].onStack = false; + V[w].onStack = false; scc[w] = adjList[w]; finished = (w == u); } while (!finished); @@ -72,7 +72,7 @@ void Tarjan::strongConnect(const T& u) { template auto Tarjan::execute() { for (const auto& u : std::views::keys(adjList)) { - if (vmap[u].index == -1) + if (V[u].index == -1) strongConnect(u); } return SCCs; diff --git a/include/graph/breadth_first_tree.h b/include/graph/breadth_first_tree.h index f77be54..197157c 100644 --- a/include/graph/breadth_first_tree.h +++ b/include/graph/breadth_first_tree.h @@ -15,7 +15,9 @@ public: BreadthFirstTree(Digraph G, T root); - T root; + void removeEdgeTo(const T& u); + + T root{}; }; template @@ -23,6 +25,18 @@ BreadthFirstTree::BreadthFirstTree(Digraph G, T root) { this->adjList = algo::BreadthFirstSearch(G.adjList).execute(root); } +template +void BreadthFirstTree::removeEdgeTo(const T& u) { + for (const auto& x : this->vertices()) { + for (const auto& y : this->adjList[x]) { + if (y == u) { + this->remove(x, u); + return; + } + } + } +} + } // namespace graph #endif \ No newline at end of file