[Feature] METIS Partition with Communication Volume Minimization (#3821)

* upd

* upd

* upd

* upd

* upd

* fix OpenMP compatibility issues

* typo

* partition

* misc

* fix typo

* num_parts=1

* import torch

* long

* print info

* print info

* print info

* upd

* remove debug code

* revert partition.py

* fix cut count

* fix cut count

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This reverts commit 10926b4fd48f45c8f1ddb58be7db6c22e653effd.

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This reverts commit 76465283bef093a2b4209ad70dd15d2437b2ec8a.

* type of deprecate

* typo in deprecate info

* fix typo

* use cv for partitioning

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* typo

* add objtype

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* fix bug

* fix bug

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This reverts commit 92b3b2f64a3a1128590098fa03ce429c5466e6ce.

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# Conflicts:
#	python/dgl/distributed/partition.py

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'"

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* Update metis_partition.cc

* Update metis_partition_hetero.cc

* Update metis_partition_hetero.cc

* Update partition.py

* Update partition.py

* Update partition.py
Co-authored-by: yzh119 <expye@outlook.com>
Co-authored-by: chwan-rice <54331508+chwan-rice@users.noreply.github.com>
Co-authored-by: Jinjing Zhou <VoVAllen@users.noreply.github.com>
Co-authored-by: Da Zheng <zhengda1936@gmail.com>

python/dgl/distributed/partition.py

@@ -293,7 +293,7 @@ def _set_trainer_ids(g, sim_g, node_parts):
 
 def partition_graph(g, graph_name, num_parts, out_path, num_hops=1, part_method="metis",
                     reshuffle=True, balance_ntypes=None, balance_edges=False, return_mapping=False,
-                    num_trainers_per_machine=1):
+                    num_trainers_per_machine=1, objtype='cut'):
     ''' Partition a graph for distributed training and store the partitions on files.
 
     The partitioning occurs in three steps: 1) run a partition algorithm (e.g., Metis) to
@@ -473,6 +473,9 @@ def partition_graph(g, graph_name, num_parts, out_path, num_hops=1, part_method=
         each node will be stored in the node feature 'trainer_id'. Then the partitions of trainers
         on the same machine will be coalesced into one larger partition. The final number of
         partitions is `num_part`.
+    objtype : str, "cut" or "vol"
+        Set the objective as edge-cut minimization or communication volume minimization. This
+        argument is used by the Metis algorithm.
 
     Returns
     -------
@@ -532,6 +535,9 @@ def partition_graph(g, graph_name, num_parts, out_path, num_hops=1, part_method=
             bal_ntypes = sim_g.ndata[NTYPE]
         return sim_g, bal_ntypes
 
+    if objtype not in ['cut', 'vol']:
+        raise ValueError
+
     if not reshuffle:
         dgl_warning("The argument reshuffle will be deprecated in the next release. "
                     "For heterogeneous graphs, reshuffle must be enabled.")
@@ -583,7 +589,7 @@ def partition_graph(g, graph_name, num_parts, out_path, num_hops=1, part_method=
                     sim_g, num_parts * num_trainers_per_machine,
                     balance_ntypes=balance_ntypes,
                     balance_edges=balance_edges,
-                    mode='k-way')
+                    mode='k-way', objtype=objtype)
                 _set_trainer_ids(g, sim_g, node_parts)
 
                 # And then coalesce the partitions of trainers on the same machine into one
@@ -592,7 +598,8 @@ def partition_graph(g, graph_name, num_parts, out_path, num_hops=1, part_method=
             else:
                 node_parts = metis_partition_assignment(sim_g, num_parts,
                                                         balance_ntypes=balance_ntypes,
-                                                        balance_edges=balance_edges)
+                                                        balance_edges=balance_edges,
+                                                        objtype=objtype)
             print('Assigning nodes to METIS partitions takes {:.3f}s, peak mem: {:.3f} GB'.format(
                 time.time() - start, get_peak_mem()))
         else:

python/dgl/partition.py

@@ -248,7 +248,8 @@ def get_peak_mem():
             return int(mem) / 1024 / 1024
     return 0.0
 
-def metis_partition_assignment(g, k, balance_ntypes=None, balance_edges=False, mode="k-way"):
+def metis_partition_assignment(g, k, balance_ntypes=None, balance_edges=False,
+                               mode="k-way", objtype='cut'):
     ''' This assigns nodes to different partitions with Metis partitioning algorithm.
 
     When performing Metis partitioning, we can put some constraint on the partitioning.
@@ -275,6 +276,9 @@ def metis_partition_assignment(g, k, balance_ntypes=None, balance_edges=False, m
         Indicate whether to balance the edges.
     mode : str, "k-way" or "recursive"
         Whether use multilevel recursive bisection or multilevel k-way paritioning.
+    objtype : str, "cut" or "vol"
+        Set the objective as edge-cut minimization or communication volume minimization. This
+        argument is used by the Metis algorithm.
 
     Returns
     -------
@@ -334,7 +338,7 @@ def metis_partition_assignment(g, k, balance_ntypes=None, balance_edges=False, m
         time.time() - start, get_peak_mem()))
 
     start = time.time()
-    node_part = _CAPI_DGLMetisPartition_Hetero(sym_g._graph, k, vwgt, mode)
+    node_part = _CAPI_DGLMetisPartition_Hetero(sym_g._graph, k, vwgt, mode, (objtype == 'cut'))
     print('Metis partitioning: {:.3f} seconds, peak memory: {:.3f} GB'.format(
         time.time() - start, get_peak_mem()))
     if len(node_part) == 0:

src/graph/metis_partition.cc

@@ -15,7 +15,7 @@ namespace dgl {
 
 #if !defined(_WIN32)
 
-IdArray MetisPartition(GraphPtr g, int k, NDArray vwgt_arr) {
+IdArray MetisPartition(GraphPtr g, int k, NDArray vwgt_arr, bool obj_cut) {
   // The index type of Metis needs to be compatible with DGL index type.
   CHECK_EQ(sizeof(idx_t), sizeof(dgl_id_t));
   ImmutableGraphPtr ig = std::dynamic_pointer_cast<ImmutableGraph>(g);
@@ -50,6 +50,12 @@ IdArray MetisPartition(GraphPtr g, int k, NDArray vwgt_arr) {
   options[METIS_OPTION_NIPARTS] = 1;
   options[METIS_OPTION_DROPEDGES] = 1;
 
+  if (obj_cut) {
+    options[METIS_OPTION_OBJTYPE] = METIS_OBJTYPE_CUT;
+  } else {
+    options[METIS_OPTION_OBJTYPE] = METIS_OBJTYPE_VOL;
+  }
+
   int ret = METIS_PartGraphKway(&nvtxs,      // The number of vertices
                                 &ncon,       // The number of balancing constraints.
                                 xadj,        // indptr
@@ -65,10 +71,17 @@ IdArray MetisPartition(GraphPtr g, int k, NDArray vwgt_arr) {
                                 &objval,      // the edge-cut or the total communication volume of
                                 // the partitioning solution
                                 part);
-  LOG(INFO) << "Partition a graph with " << g->NumVertices()
-      << " nodes and " << g->NumEdges()
-      << " edges into " << k
-      << " parts and get " << objval << " edge cuts";
+
+  if (obj_cut) {
+    LOG(INFO) << "Partition a graph with " << g->NumVertices() << " nodes and "
+              << g->NumEdges() << " edges into " << k << " parts and "
+              << "get " << objval << " edge cuts";
+  } else {
+    LOG(INFO) << "Partition a graph with " << g->NumVertices() << " nodes and "
+              << g->NumEdges() << " edges into " << k << " parts and "
+              << "the communication volume is " << objval;
+  }
+
   switch (ret) {
     case METIS_OK:
       return part_arr;
@@ -90,8 +103,9 @@ DGL_REGISTER_GLOBAL("transform._CAPI_DGLMetisPartition")
     GraphRef g = args[0];
     int k = args[1];
     NDArray vwgt = args[2];
+    bool obj_cut = args[3];
 #if !defined(_WIN32)
-    *rv = MetisPartition(g.sptr(), k, vwgt);
+    *rv = MetisPartition(g.sptr(), k, vwgt, obj_cut);
 #else
     LOG(FATAL) << "Metis partition does not support Windows.";
 #endif  // !defined(_WIN32)

src/graph/transform/metis_partition_hetero.cc

@@ -19,7 +19,8 @@ namespace transform {
 
 #if !defined(_WIN32)
 
-IdArray MetisPartition(UnitGraphPtr g, int k, NDArray vwgt_arr, const std::string &mode) {
+IdArray MetisPartition(UnitGraphPtr g, int k, NDArray vwgt_arr,
+                       const std::string &mode, bool obj_cut) {
   // Mode can only be "k-way" or "recursive"
   CHECK(mode == "k-way" || mode == "recursive")
     << "mode can only be \"k-way\" or \"recursive\"";
@@ -59,6 +60,12 @@ IdArray MetisPartition(UnitGraphPtr g, int k, NDArray vwgt_arr, const std::strin
   options[METIS_OPTION_NIPARTS] = 1;
   options[METIS_OPTION_DROPEDGES] = 1;
 
+  if (obj_cut) {
+    options[METIS_OPTION_OBJTYPE] = METIS_OBJTYPE_CUT;
+  } else {
+    options[METIS_OPTION_OBJTYPE] = METIS_OBJTYPE_VOL;
+  }
+
   int ret = partition_func(
     &nvtxs,  // The number of vertices
     &ncon,   // The number of balancing constraints.
@@ -75,9 +82,17 @@ IdArray MetisPartition(UnitGraphPtr g, int k, NDArray vwgt_arr, const std::strin
     &objval,  // the edge-cut or the total communication volume of
     // the partitioning solution
     part);
-  LOG(INFO) << "Partition a graph with " << g->NumVertices(0) << " nodes and "
-            << g->NumEdges(0) << " edges into " << k << " parts and get "
-            << objval << " edge cuts";
+
+  if (obj_cut) {
+    LOG(INFO) << "Partition a graph with " << g->NumVertices(0) << " nodes and "
+              << g->NumEdges(0) << " edges into " << k << " parts and "
+              << "get " << objval << " edge cuts";
+  } else {
+    LOG(INFO) << "Partition a graph with " << g->NumVertices(0) << " nodes and "
+              << g->NumEdges(0) << " edges into " << k << " parts and "
+              << "the communication volume is " << objval;
+  }
+
   switch (ret) {
     case METIS_OK:
       return part_arr;
@@ -105,8 +120,9 @@ DGL_REGISTER_GLOBAL("partition._CAPI_DGLMetisPartition_Hetero")
     int k = args[1];
     NDArray vwgt = args[2];
     std::string mode = args[3];
+    bool obj_cut = args[4];
 #if !defined(_WIN32)
-    *rv = MetisPartition(ugptr, k, vwgt, mode);
+    *rv = MetisPartition(ugptr, k, vwgt, mode, obj_cut);
 #else
     LOG(FATAL) << "Metis partition does not support Windows.";
 #endif  // !defined(_WIN32)