Graph_Coloring.H

Go to the documentation of this file.

/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
#ifndef GRAPH_COLORING_H
#define GRAPH_COLORING_H
 
#include <tpl_graph.H>
#include <tpl_array.H>
#include <tpl_dynMapTree.H>
#include <tpl_dynSetTree.H>
#include <tpl_sort_utils.H>
#include <cookie_guard.H>
#include <ah-errors.H>
 
namespace Aleph {
 
namespace graph_coloring_detail {
 
inline void *encode_color(size_t c) noexcept
{
  return reinterpret_cast<void *>(static_cast<uintptr_t>(c + 1));
}
 
inline bool is_colored(void *cookie) noexcept
{
  return cookie != nullptr;
}
 
inline size_t decode_color(void *cookie) noexcept
{
  return static_cast<size_t>(reinterpret_cast<uintptr_t>(cookie)) - 1;
}
 
inline size_t smallest_available(const DynSetTree<size_t> &used)
{
  size_t c = 0;
  while (used.search(c) != nullptr)
    ++c;
  return c;
}
 
template <class GT, class SA>
void build_undirected_adj(const GT                                                      &g,
                          DynMapTree<typename GT::Node *, DynList<typename GT::Node *>> &adj)
{
  using Node = typename GT::Node;
 
  // Ensure all nodes are present in the adjacency map with empty lists.
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    adj.insert(it.get_curr(), DynList<Node *>());
 
  // Temporary per-node neighbor sets to deduplicate parallel arcs.
  DynMapTree<Node *, DynSetTree<Node *>> neighbor_sets;
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    neighbor_sets.insert(it.get_curr(), DynSetTree<Node *>());
 
  // Collect undirected neighbors, deduplicating parallel arcs.
  for (auto it = g.get_arc_it(); it.has_curr(); it.next_ne())
    {
      auto *arc = it.get_curr();
      if (not SA()(arc))
        continue;
      Node *u = g.get_src_node(arc);
      Node *v = g.get_tgt_node(arc);
      if (u == v)
        continue;
      neighbor_sets[u].insert(v);
      neighbor_sets[v].insert(u);
    }
 
  // Materialize deduplicated neighbor sets into adjacency lists.
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    {
      Node *u        = it.get_curr();
      auto &adj_list = adj[u];
      auto &nbrs     = neighbor_sets[u];
      for (auto sit = nbrs.get_it(); sit.has_curr(); sit.next_ne())
        adj_list.append(sit.get_curr());
    }
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
void validate_no_self_loops(const GT &g)
{
  for (auto it = g.get_arc_it(); it.has_curr(); it.next_ne())
    {
      auto *arc = it.get_curr();
      ah_domain_error_if(SA()(arc) and g.get_src_node(arc) == g.get_tgt_node(arc))
        << "graph coloring does not support self-loops";
    }
}
 
}  // end namespace graph_coloring_detail
 
template <class GT, class SA = Dft_Show_Arc<GT>>
size_t greedy_coloring(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors)
{
  using Node = typename GT::Node;
  using namespace graph_coloring_detail;
 
  colors = {};
  if (g.get_num_nodes() == 0)
    return 0;
 
  validate_no_self_loops<GT, SA>(g);
 
  DynMapTree<Node *, DynList<Node *>> adj;
  build_undirected_adj<GT, SA>(g, adj);
 
  Cookie_Saver<GT> saver(g, true, false);
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    NODE_COOKIE(it.get_curr()) = nullptr;
 
  size_t num_colors = 0;
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    {
      Node              *v = it.get_curr();
      DynSetTree<size_t> used;
 
      for (auto nit = adj[v].get_it(); nit.has_curr(); nit.next_ne())
        if (Node *w = nit.get_curr(); is_colored(NODE_COOKIE(w)))
          used.insert(decode_color(NODE_COOKIE(w)));
 
      size_t c       = smallest_available(used);
      NODE_COOKIE(v) = encode_color(c);
      colors.insert(v, c);
 
      if (c + 1 > num_colors)
        num_colors = c + 1;
    }
 
  return num_colors;
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
size_t welsh_powell_coloring(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors)
{
  using Node = typename GT::Node;
  using namespace graph_coloring_detail;
 
  colors = {};
  if (g.get_num_nodes() == 0)
    return 0;
 
  validate_no_self_loops<GT, SA>(g);
 
  DynMapTree<Node *, DynList<Node *>> adj;
  build_undirected_adj<GT, SA>(g, adj);
 
  Cookie_Saver<GT> saver(g, true, false);
  DynList<Node *>  nodes;
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    {
      Node *p        = it.get_curr();
      NODE_COOKIE(p) = nullptr;
      nodes.append(p);
    }
 
  mergesort(nodes, [&adj](Node *a, Node *b)
  {
    return adj[a].size() > adj[b].size();
  });
 
  size_t num_colors = 0;
  for (auto nit = nodes.get_it(); nit.has_curr(); nit.next_ne())
    {
      Node              *v = nit.get_curr();
      DynSetTree<size_t> used;
 
      for (auto ait = adj[v].get_it(); ait.has_curr(); ait.next_ne())
        {
          Node *w = ait.get_curr();
          if (is_colored(NODE_COOKIE(w)))
            used.insert(decode_color(NODE_COOKIE(w)));
        }
 
      size_t c       = smallest_available(used);
      NODE_COOKIE(v) = encode_color(c);
      colors.insert(v, c);
 
      if (c + 1 > num_colors)
        num_colors = c + 1;
    }
 
  return num_colors;
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
size_t dsatur_coloring(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors)
{
  using Node = typename GT::Node;
  using namespace graph_coloring_detail;
 
  colors = {};
  if (const size_t n = g.get_num_nodes(); n == 0)
    return 0;
 
  validate_no_self_loops<GT, SA>(g);
 
  DynMapTree<Node *, DynList<Node *>> adj;
  build_undirected_adj<GT, SA>(g, adj);
 
  Cookie_Saver<GT>                       saver(g, true, false);
  DynMapTree<Node *, DynSetTree<size_t>> saturation_sets;
  DynSetTree<Node *>                     uncolored_nodes;
 
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    {
      Node *v        = it.get_curr();
      NODE_COOKIE(v) = nullptr;
      uncolored_nodes.insert(v);
      saturation_sets.insert(v, DynSetTree<size_t>());
    }
 
  size_t num_colors = 0;
  while (not uncolored_nodes.is_empty())
    {
      Node  *best     = nullptr;
      size_t best_sat = 0;
      size_t best_deg = 0;
 
      // Select best node: O(V)
      for (auto it = uncolored_nodes.get_it(); it.has_curr(); it.next_ne())
        {
          Node  *v   = it.get_curr();
          size_t sat = saturation_sets[v].size();
          size_t deg = adj[v].size();
 
          if (best == nullptr or sat > best_sat or (sat == best_sat and deg > best_deg))
            {
              best     = v;
              best_sat = sat;
              best_deg = deg;
            }
        }
 
      size_t c          = smallest_available(saturation_sets[best]);
      NODE_COOKIE(best) = encode_color(c);
      colors.insert(best, c);
      uncolored_nodes.remove(best);
 
      if (c + 1 > num_colors)
        num_colors = c + 1;
 
      // Update neighbors: O(deg(best) log colors)
      for (auto it = adj[best].get_it(); it.has_curr(); it.next_ne())
        if (Node *w = it.get_curr(); not is_colored(NODE_COOKIE(w)))
          saturation_sets[w].insert(c);
    }
 
  return num_colors;
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
[[nodiscard]] bool is_valid_coloring(const GT                                      &g,
                                     const DynMapTree<typename GT::Node *, size_t> &colors)
{
  using Node = typename GT::Node;
 
  // Explicit per-node check: every graph node must have a color entry.
  // A size match alone is insufficient — the map could be keyed with
  // foreign pointers that coincidentally match the node count.
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    if (colors.search(it.get_curr()) == nullptr)
      return false;
 
  for (auto it = g.get_arc_it(); it.has_curr(); it.next_ne())
    {
      auto *arc = it.get_curr();
      if (not SA()(arc))
        continue;
      Node *u = g.get_src_node(arc);
      Node *v = g.get_tgt_node(arc);
      if (u == v)
        return false;
      auto *pu = colors.search(u);
      auto *pv = colors.search(v);
      if (pu == nullptr or pv == nullptr)
        return false;
      if (pu->second == pv->second)
        return false;
    }
 
  return true;
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
size_t chromatic_number(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors)
{
  using Node = typename GT::Node;
  using namespace graph_coloring_detail;
 
  ah_domain_error_if(g.get_num_nodes() > 64)
    << "chromatic_number: graph has " << g.get_num_nodes() << " nodes (max 64)";
 
  colors = {};
  if (g.get_num_nodes() == 0)
    return 0;
 
  validate_no_self_loops<GT, SA>(g);
 
  DynMapTree<Node *, size_t> best_colors;
  size_t                     upper = dsatur_coloring<GT, SA>(g, best_colors);
 
  if (upper <= 2)
    {
      colors = std::move(best_colors);
      return upper;
    }
 
  DynList<Node *> node_list;
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    node_list.append(it.get_curr());
 
  const size_t  n = node_list.size();
  Array<Node *> nodes(n, nullptr);
  size_t        idx = 0;
  for (auto it = node_list.get_it(); it.has_curr(); it.next_ne())
    nodes[idx++] = it.get_curr();
 
  Array<DynList<size_t>> adj_idx(n, DynList<size_t>{});
  {
    Cookie_Saver<GT> saver(g, true, false);
    for (size_t i = 0; i < n; ++i)
      NODE_COOKIE(nodes[i]) = reinterpret_cast<void *>(static_cast<uintptr_t>(i));
 
    for (auto it = g.get_arc_it(); it.has_curr(); it.next_ne())
      {
        auto *arc = it.get_curr();
        if (not SA()(arc))
          continue;
        size_t i = reinterpret_cast<uintptr_t>(NODE_COOKIE(g.get_src_node(arc)));
        size_t j = reinterpret_cast<uintptr_t>(NODE_COOKIE(g.get_tgt_node(arc)));
        if (i != j)
          {
            adj_idx[i].append(j);
            adj_idx[j].append(i);
          }
      }
  }
 
  Array<size_t> coloring(n, static_cast<size_t>(0));
  auto          reset_coloring = [&]()
  {
    for (size_t i = 0; i < n; ++i)
      coloring[i] = 0;
  };
 
  auto try_k_coloring = [&](size_t k, auto &self, size_t node_idx) -> bool
  {
    if (node_idx == n)
      return true;
    for (size_t c = 0; c < k; ++c)
      {
        bool feasible = true;
        for (auto jit = adj_idx[node_idx].get_it(); jit.has_curr(); jit.next_ne())
          {
            size_t j = jit.get_curr();
            if (j < node_idx and coloring[j] == c)
              {
                feasible = false;
                break;
              }
          }
        if (feasible)
          {
            coloring[node_idx] = c;
            if (self(k, self, node_idx + 1))
              return true;
          }
      }
    coloring[node_idx] = 0;
    return false;
  };
 
  size_t lo = 2, hi = upper;
  while (lo < hi)
    {
      size_t mid = (lo + hi) / 2;
      reset_coloring();
      if (try_k_coloring(mid, try_k_coloring, 0))
        hi = mid;
      else
        lo = mid + 1;
    }
 
  if (lo < upper)
    {
      reset_coloring();
      try_k_coloring(lo, try_k_coloring, 0);
      colors = {};
      for (size_t i = 0; i < n; ++i)
        colors.insert(nodes[i], coloring[i]);
    }
  else
    colors = std::move(best_colors);
 
  return lo;
}
 
template <class GT, class SA = Dft_Show_Arc<GT>>
class Greedy_Coloring
{
public:
  size_t operator()(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors) const
  {
    return greedy_coloring<GT, SA>(g, colors);
  }
};
 
template <class GT, class SA = Dft_Show_Arc<GT>>
class Welsh_Powell_Coloring
{
public:
  size_t operator()(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors) const
  {
    return welsh_powell_coloring<GT, SA>(g, colors);
  }
};
 
template <class GT, class SA = Dft_Show_Arc<GT>>
class DSatur_Coloring
{
public:
  size_t operator()(const GT &g, DynMapTree<typename GT::Node *, size_t> &colors) const
  {
    return dsatur_coloring<GT, SA>(g, colors);
  }
};
 
}  // end namespace Aleph
 
#endif  // GRAPH_COLORING_H