From 42f824a2496464595ab5b412927d3e4b8e5d4602 Mon Sep 17 00:00:00 2001 From: stefiosif Date: Mon, 12 Sep 2022 00:08:45 +0300 Subject: [PATCH] Update decremental scc algorithm --- algorithm/decremental_scc.h | 58 +++++++------- algorithm/tarjan.h | 2 +- test/decremental_test.cc | 148 ++++++------------------------------ 3 files changed, 57 insertions(+), 151 deletions(-) diff --git a/algorithm/decremental_scc.h b/algorithm/decremental_scc.h index bc56866..37de51e 100644 --- a/algorithm/decremental_scc.h +++ b/algorithm/decremental_scc.h @@ -3,25 +3,30 @@ #include "algorithm/roditty_zwick.h" #include "algorithm/tarjan.h" -#include "tree/breadth_first_tree.h" +#include "graph/breadth_first_tree.h" using namespace graph; -using namespace tree; namespace algo { template class DecrementalSCC : public RodittyZwick { public: + DecrementalSCC() = default; + DecrementalSCC(Digraph G) : G(G) {} void init(); void findSCC(); + // Return true if u and v are in the same SCC bool query(const T& u, const T& v); + // Remove edge (u,v) and update A accordingly for fast checking query void remove(const T& u, const T& v); + + void setGraph(Digraph G); private: Digraph G; @@ -33,7 +38,7 @@ private: std::map> outTree; // Connect each representative with its SCC - std::map> connection; + std::map> SCC; }; template @@ -43,20 +48,18 @@ void DecrementalSCC::init() { template void DecrementalSCC::findSCC() { - auto SCCs = Tarjan(G).execute(); - + auto SCCs = Tarjan(G.adjMatrix).execute(); + for (auto& C : SCCs) { - const auto& w = C.representative(); + const auto& w = C.id; - for (const auto& v : C.adjMatrix) - A[v.first] = w; + for (const auto& v : std::views::keys(C.adjMatrix)) + A[v] = w; - outTree[w] = - BreadthFirstTree(BreadthFirstSearch(C).execute(w)); - inTree[w] = - BreadthFirstTree(BreadthFirstSearch(C.reverse()).execute(w)); + outTree[w] = BreadthFirstTree(C, w); + inTree[w] = BreadthFirstTree(C.reverse(), w); - connection[w] = C; + SCC[w] = C; } } @@ -67,27 +70,30 @@ bool DecrementalSCC::query(const T& u, const T& v) { template void DecrementalSCC::remove(const T& u, const T& v) { - G.adjMatrix[u].erase(v); + const auto& w = A[u]; + SCC[w].remove(u, v); + G.remove(u, v); // If u and v are not in the same SCC, do nothing if (A[u] != A[v]) return; - const auto& w = A[u]; - connection[w].remove(u, v); + // If edge (u,v) is not contained in both inTree and outTree do nothing + if (!inTree[w].adjMatrix[u].contains(v) && + !outTree[w].adjMatrix[u].contains(v)) + return; - // Update In(w) and Out(w) if they contain the edge - if (inTree[w].contains(u, v) || outTree[w].contains(u, v)) { - auto C = connection[w]; - inTree[w] = - BreadthFirstTree(BreadthFirstSearch(C.reverse()).execute(w)); - outTree[w] = - BreadthFirstTree(BreadthFirstSearch(C).execute(w)); - } + // Update In(w) and Out(w) + outTree[w] = BreadthFirstTree(SCC[w], w); + inTree[w] = BreadthFirstTree(SCC[w].reverse(), w); // If a SCC is broken, compute all SCCs again - if (!inTree[w].contains(u) || !outTree[w].contains(v)) { + if (!inTree[w].adjMatrix.count(u) || !outTree[w].adjMatrix.count(v)) findSCC(); - } +} + +template +void DecrementalSCC::setGraph(Digraph G) { + this->G = G; } }; // namespace algo diff --git a/algorithm/tarjan.h b/algorithm/tarjan.h index 17bcbb8..f0e0245 100644 --- a/algorithm/tarjan.h +++ b/algorithm/tarjan.h @@ -65,7 +65,7 @@ void Tarjan::strongConnect(const T& u) { finished = (w == u); } while (!finished); - SCCs.push_back({ scc, static_cast(vmap[u].lowlink) }); + SCCs.push_back({ scc, static_cast(vmap[u].lowlink + 1) }); } } diff --git a/test/decremental_test.cc b/test/decremental_test.cc index e7d14d2..8f839f6 100644 --- a/test/decremental_test.cc +++ b/test/decremental_test.cc @@ -8,48 +8,11 @@ using namespace graph; TEST_SUITE("Decremental algorithms") { - TEST_CASE("Decremental maintenance of SCCs 1") { - // 1 --> 2 --> 5 --> 7 --> 2 - // 1 --> 4 --> 3 --> 1 - // 4 --> 6 --> 3 - Digraph G; - G.insert(1, 2); - G.insert(1, 4); - G.insert(2, 5); - G.insert(3, 1); - G.insert(4, 3); - G.insert(4, 6); - G.insert(5, 7); - G.insert(6, 3); - G.insert(7, 2); - - REQUIRE_EQ(G.adjMatrix.size(), 7); - - algo::DecrementalSCC rz(G); - rz.init(); - - SUBCASE("DecrementalSCC::query") { - CHECK_EQ(rz.query(1, 2), false); - CHECK_EQ(rz.query(1, 3), true); - CHECK_EQ(rz.query(1, 7), false); - CHECK_EQ(rz.query(2, 3), false); - CHECK_EQ(rz.query(2, 5), true); - CHECK_EQ(rz.query(5, 7), true); - } - - SUBCASE("DecrementalSCC::remove") { - rz.remove(4,3); - CHECK_EQ(rz.query(4, 3), true); - - rz.remove(2, 5); - CHECK_EQ(rz.query(5, 7), false); - } - } - - TEST_CASE("Decremental maintenance of SCCs 2") { + TEST_CASE("Decremental maintenance of SCCs") { // 1 --> 2 --> 3 --> 1 // 3 --> 4 --> 5 --> 3 // 2 --> 6 --> 7 --> 8 --> 6 + // 7 --> 9 // 6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9 // 12 --> 10 Digraph G; @@ -74,61 +37,38 @@ TEST_SUITE("Decremental algorithms") { REQUIRE_EQ(G.adjMatrix.size(), 13); - algo::DecrementalSCC rz(G); - rz.init(); - + algo::DecrementalSCC decremental(G); + decremental.init(); + SUBCASE("DecrementalSCC::query") { - CHECK_EQ(rz.query(1, 2), true); - CHECK_EQ(rz.query(1, 3), true); - CHECK_EQ(rz.query(1, 7), false); - CHECK_EQ(rz.query(2, 3), true); - CHECK_EQ(rz.query(2, 13), false); - CHECK_EQ(rz.query(11, 9), true); + CHECK_EQ(decremental.query(1, 5), true); + CHECK_EQ(decremental.query(1, 7), false); + CHECK_EQ(decremental.query(1, 9), false); } SUBCASE("DecrementalSCC::remove") { - rz.remove(12, 10); - CHECK_EQ(rz.query(12, 10), true); + decremental.remove(12, 10); - rz.remove(3, 4); - CHECK_EQ(rz.query(2, 5), false); - CHECK_EQ(rz.query(1, 3), true); + CHECK_EQ(decremental.query(12, 10), true); + CHECK_EQ(decremental.query(11, 10), true); + + decremental.remove(9, 10); + + CHECK_EQ(decremental.query(12, 13), false); + CHECK_EQ(decremental.query(10, 12), false); + + decremental.remove(2, 6); + + CHECK_EQ(decremental.query(5, 8), false); + CHECK_EQ(decremental.query(6, 8), true); } } - TEST_CASE("Italiano 1") { - // 1 --> 2 --> 5 --> 7 --> 2 - // 1 --> 4 --> 3 --> 1 - // 4 --> 6 --> 3 - Digraph G; - G.insert(1, 2); - G.insert(1, 4); - G.insert(2, 5); - G.insert(3, 1); - G.insert(4, 3); - G.insert(4, 6); - G.insert(5, 7); - G.insert(6, 3); - G.insert(7, 2); - - REQUIRE_EQ(G.adjMatrix.size(), 7); - - algo::Italiano rz(G); - rz.init(); - - SUBCASE("Italiano::query") { - - } - - SUBCASE("Italiano::remove") { - - } - } - - TEST_CASE("Italiano 2") { + TEST_CASE("Italiano") { // 1 --> 2 --> 3 --> 1 // 3 --> 4 --> 5 --> 3 // 2 --> 6 --> 7 --> 8 --> 6 + // 7 --> 9 // 6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9 // 12 --> 10 Digraph G; @@ -169,6 +109,7 @@ TEST_SUITE("Decremental algorithms") { // 1 --> 2 --> 3 --> 1 // 3 --> 4 --> 5 --> 3 // 2 --> 6 --> 7 --> 8 --> 6 + // 7 --> 9 // 6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9 // 12 --> 10 Digraph G; @@ -204,45 +145,4 @@ TEST_SUITE("Decremental algorithms") { } } - - TEST_CASE("Frigioni 2") { - // 1 --> 2 --> 3 --> 1 - // 3 --> 4 --> 5 --> 3 - // 2 --> 6 --> 7 --> 8 --> 6 - // 6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9 - // 12 --> 10 - Digraph G; - G.insert(1, 2); - G.insert(2, 3); - G.insert(3, 1); - G.insert(3, 4); - G.insert(4, 5); - G.insert(5, 3); - G.insert(2, 6); - G.insert(6, 7); - G.insert(7, 8); - G.insert(7, 9); - G.insert(8, 6); - G.insert(6, 9); - G.insert(9, 10); - G.insert(10, 11); - G.insert(11, 12); - G.insert(12, 13); - G.insert(13, 9); - G.insert(12, 10); - - REQUIRE_EQ(G.adjMatrix.size(), 13); - - algo::Frigioni rz(G); - rz.init(); - - SUBCASE("Frigioni::query") { - - } - - SUBCASE("Frigioni::remove") { - - } - } - } \ No newline at end of file