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jet_refiner.hpp
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jet_refiner.hpp
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// ***********************************************************************
//
// Jet: Multilevel Graph Partitioning
//
// Copyright 2023 National Technology & Engineering Solutions of Sandia, LLC
// (NTESS).
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// ************************************************************************
#pragma once
#include <type_traits>
#include <limits>
#include <iostream>
#include <iomanip>
#include <Kokkos_Core.hpp>
#include "KokkosSparse_CrsMatrix.hpp"
#include "ExperimentLoggerUtil.hpp"
#include "part_stat.hpp"
namespace jet_partitioner {
template<class crsMat, typename part_t>
class jet_refiner {
public:
//helper for getting gain_t
template<typename T>
struct type_identity {
typedef T type;
};
// define internal types
using matrix_t = crsMat;
using exec_space = typename matrix_t::execution_space;
using mem_space = typename matrix_t::memory_space;
using Device = typename matrix_t::device_type;
using ordinal_t = typename matrix_t::ordinal_type;
using edge_offset_t = typename matrix_t::size_type;
using scalar_t = typename matrix_t::value_type;
// need some trickery because make_signed is undefined for floating point types
using gain_t = typename std::conditional_t<std::is_signed_v<scalar_t>, type_identity<scalar_t>, std::make_signed<scalar_t>>::type;
using vtx_view_t = Kokkos::View<ordinal_t*, Device>;
using vtx_svt = Kokkos::View<ordinal_t, Device>;
using wgt_view_t = Kokkos::View<scalar_t*, Device>;
using edge_view_t = Kokkos::View<edge_offset_t*, Device>;
using gain_vt = Kokkos::View<gain_t*, Device>;
using gain_svt = Kokkos::View<gain_t, Device>;
using part_vt = Kokkos::View<part_t*, Device>;
using part_svt = Kokkos::View<part_t, Device>;
using edge_subview_t = Kokkos::View<edge_offset_t, Device>;
using policy_t = Kokkos::RangePolicy<exec_space>;
using team_policy_t = Kokkos::TeamPolicy<exec_space>;
using member = typename team_policy_t::member_type;
using stat = part_stat<matrix_t, part_t>;
static constexpr ordinal_t ORD_MAX = std::numeric_limits<ordinal_t>::max();
static constexpr gain_t GAIN_MIN = std::numeric_limits<gain_t>::lowest();
static constexpr bool is_host_space = std::is_same<typename exec_space::memory_space, typename Kokkos::DefaultHostExecutionSpace::memory_space>::value;
static constexpr part_t NULL_PART = -1;
static constexpr part_t HASH_RECLAIM = -2;
static const ordinal_t max_sections = 128;
static const int max_buckets = 50;
static const int mid_bucket = 25;
//data that is preserved between levels in the multilevel scheme
struct refine_data {
gain_vt part_sizes;
scalar_t total_size = 0;
gain_t cut = 0;
gain_t total_imb = 0;
bool init = false;
};
struct problem {
matrix_t g;
wgt_view_t vtx_w;
part_t k;
double imb;
ordinal_t opt;
ordinal_t size_max;
};
//vertex-part connectivity data
struct conn_data {
gain_vt conn_vals;
edge_view_t conn_offsets;
vtx_view_t lock_bit;
part_vt dest_cache;
part_vt conn_entries;
part_vt conn_table_sizes;
};
//this struct contains all the scratch memory used by the refinement iterations
struct scratch_mem {
gain_vt gain1, gain2, gain_persistent, evict_start, evict_end;
vtx_view_t vtx1, vtx2, zeros1;
part_vt dest_part, undersized;
vtx_svt counter1;
gain_svt cut_change1, cut_change2, max_part;
gain_vt reduce_locs;
typename gain_vt::HostMirror reduce_copy;
part_svt total_undersized;
scratch_mem(const ordinal_t n, const ordinal_t min_size, const part_t k) {
gain1 = gain_vt(Kokkos::ViewAllocateWithoutInitializing("gain scratch 1"), std::max(n, min_size));
gain2 = gain_vt(Kokkos::ViewAllocateWithoutInitializing("gain scratch 2"), n);
gain_persistent = gain_vt(Kokkos::ViewAllocateWithoutInitializing("gain persistent"), n);
evict_start = gain_vt("evict start", k);
evict_end = gain_vt("evict end", k);
undersized = part_vt("undersized parts", k);
vtx1 = vtx_view_t(Kokkos::ViewAllocateWithoutInitializing("vtx scratch 1"), n);
vtx2 = vtx_view_t(Kokkos::ViewAllocateWithoutInitializing("vtx scratch 2"), std::max(n, min_size));
dest_part = part_vt(Kokkos::ViewAllocateWithoutInitializing("destination scratch"), n);
zeros1 = vtx_view_t("zeros 1", n);
counter1 = vtx_svt("counter 1");
total_undersized = part_svt("total undersized");
reduce_locs = gain_vt("reduce to here", 3);
reduce_copy = Kokkos::create_mirror_view(reduce_locs);
cut_change1 = Kokkos::subview(reduce_locs, 0);
cut_change2 = Kokkos::subview(reduce_locs, 1);
max_part = Kokkos::subview(reduce_locs, 2);
}
};
scratch_mem perm_scratch;
conn_data perm_cdata;
//find maximum size for conn_entries and conn_vals
edge_offset_t count_gain_size(const matrix_t largest, part_t k){
edge_offset_t gain_size = 0;
Kokkos::parallel_reduce("comp offsets", policy_t(0, largest.numRows()), KOKKOS_LAMBDA(const ordinal_t& i, edge_offset_t& update){
ordinal_t degree = largest.graph.row_map(i + 1) - largest.graph.row_map(i);
if(degree > static_cast<ordinal_t>(k)) degree = k;
update += degree;
}, gain_size);
return gain_size;
}
jet_refiner(const matrix_t largest, part_t k) :
perm_scratch(largest.numRows(), k*max_sections*max_buckets, k) {
ordinal_t n = largest.numRows();
edge_view_t conn_offsets("gain offsets", n + 1);
edge_offset_t gain_size = count_gain_size(largest, k);
perm_cdata.conn_vals = gain_vt(Kokkos::ViewAllocateWithoutInitializing("conn vals"), gain_size);
perm_cdata.conn_entries = part_vt(Kokkos::ViewAllocateWithoutInitializing("conn entries"), gain_size);
perm_cdata.conn_offsets = conn_offsets;
perm_cdata.dest_cache = part_vt(Kokkos::ViewAllocateWithoutInitializing("best connected part for each vertex"), n);
perm_cdata.conn_table_sizes = part_vt(Kokkos::ViewAllocateWithoutInitializing("map size"), n);
perm_cdata.lock_bit = vtx_view_t("lock bit", n);
}
void copy_refine_data(refine_data& lhs, refine_data& rhs){
Kokkos::deep_copy(exec_space(), lhs.part_sizes, rhs.part_sizes);
lhs.total_size = rhs.total_size;
lhs.cut = rhs.cut;
lhs.total_imb = rhs.total_imb;
lhs.init = rhs.init;
}
refine_data clone_refine_data(refine_data& rhs){
refine_data clone;
clone.part_sizes = gain_vt(Kokkos::ViewAllocateWithoutInitializing("part sizes"), rhs.part_sizes.extent(0));
copy_refine_data(clone, rhs);
return clone;
}
//determines which vertices (if any) should be moved to another part to decrease cutsize
//8 kernels, 2 device-host syncs
vtx_view_t jet_lp(const problem& prob, const part_vt& part, const conn_data& cdata, scratch_mem& scratch, double filter_ratio){
const matrix_t& g = prob.g;
ordinal_t n = g.numRows();
ordinal_t num_pos = 0;
vtx_view_t swap_scratch = scratch.vtx1;
part_vt dest_part = scratch.dest_part;
part_vt conn_entries = cdata.conn_entries;
edge_view_t conn_offsets = cdata.conn_offsets;
gain_vt conn_vals = cdata.conn_vals;
gain_vt save_gains = scratch.gain_persistent;
vtx_view_t lock_bit = cdata.lock_bit;
Kokkos::parallel_for("select destination part (lp)", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i){
part_t best = cdata.dest_cache(i);
if(best != NULL_PART) {
dest_part(i) = best;
return;
}
part_t p = part(i);
best = p;
gain_t b_conn = 0;
gain_t p_conn = 0;
edge_offset_t start = conn_offsets(i);
part_t size = cdata.conn_table_sizes(i);
edge_offset_t end = start + size;
//finds potential destination as most connected part excluding p
for(edge_offset_t j = start; j < end; j++){
gain_t j_conn = conn_vals(j);
if(j_conn > b_conn && conn_entries(j) != p){
best = conn_entries(j);
b_conn = j_conn;
} else if(j_conn > 0 && conn_entries(j) == p){
p_conn = j_conn;
}
}
save_gains(i) = 0;
if(best != p){
// vertices must pass this filter in order to be considered further
// b_conn >= p_conn may seem redundant but it is important
// to address an edge case where floor(filter_ratio*p_conn) rounds to zero
if(b_conn >= p_conn || ((p_conn - b_conn) < floor(filter_ratio*p_conn))){
save_gains(i) = b_conn - p_conn;
} else {
best = p;
}
}
cdata.dest_cache(i) = best;
//a vertex is not considered further if best == p
dest_part(i) = best;
});
//need to store the pre-afterburn gains into a separate view
//than savegains, because we write new values into it that may not be overwritten
//if a vertex has its best neighbor cached
gain_vt pregain = scratch.gain1;
//write all unlocked vertices that passed the above filter into an unordered list
//output count of such vertices into num_pos
Kokkos::parallel_scan("filter potentially viable moves", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i, ordinal_t& update, const bool final){
part_t p = part(i);
part_t best = dest_part(i);
if(p != best && lock_bit(i) == 0){
if(final){
swap_scratch(update) = i;
pregain(i) = save_gains(i);
}
update++;
} else if(final){
pregain(i) = GAIN_MIN;
lock_bit(i) = 0;
}
}, num_pos);
//truncate scratch views by num_pos
vtx_view_t pos_moves = Kokkos::subview(swap_scratch, std::make_pair(static_cast<ordinal_t>(0), num_pos));
//in this kernel every potential move from the previous filters
//is reevaluated by considering the effect of the other potential moves
//a move is considered to occur before another according to their potential gains
//and the vertex ids
Kokkos::parallel_for("afterburner heuristic", team_policy_t(num_pos, Kokkos::AUTO), KOKKOS_LAMBDA(const member& t){
gain_t change = 0;
ordinal_t i = pos_moves(t.league_rank());
part_t best = dest_part(i);
part_t p = part(i);
gain_t igain = pregain(i);
Kokkos::parallel_reduce(Kokkos::TeamThreadRange(t, g.graph.row_map(i), g.graph.row_map(i + 1)), [&](const edge_offset_t j, gain_t& update){
ordinal_t v = g.graph.entries(j);
gain_t vgain = pregain(v);
//adjust local gain if v has higher priority than i
if(vgain > igain || (vgain == igain && v < i)){
part_t vpart = dest_part(v);
scalar_t wgt = g.values(j);
if(vpart == p){
update -= wgt;
} else if(vpart == best){
update += wgt;
}
vpart = part(v);
if(vpart == p){
update += wgt;
} else if(vpart == best){
update -= wgt;
}
}
}, change);
t.team_barrier();
Kokkos::single(Kokkos::PerTeam(t), [&](){
if(igain + change >= 0){
lock_bit(i) = 1;
}
});
});
vtx_view_t swaps2 = Kokkos::subview(scratch.vtx2, std::make_pair(static_cast<ordinal_t>(0), num_pos));
//scan all vertices that passed the post filter
Kokkos::parallel_scan("filter beneficial moves", policy_t(0, num_pos), KOKKOS_LAMBDA(const ordinal_t i, ordinal_t& update, const bool final){
ordinal_t v = pos_moves(i);
if(lock_bit(v)){
if(final){
swaps2(update) = v;
}
update++;
}
}, num_pos);
pos_moves = Kokkos::subview(swaps2, std::make_pair(static_cast<ordinal_t>(0), num_pos));
return pos_moves;
}
KOKKOS_INLINE_FUNCTION
static ordinal_t gain_bucket(const gain_t& gx, const scalar_t& vwgt){
//cast to float so we can approximate log_1.5
float gain = static_cast<float>(gx) / static_cast<float>(vwgt);
ordinal_t gain_type = 0;
if(gain > 0.0){
gain_type = 0;
} else if(gain == 0.0) {
gain_type = 1;
} else {
gain_type = mid_bucket;
gain = abs(gain);
if(gain < 1.0){
while(gain < 1.0){
gain *= 1.5;
gain_type--;
}
if(gain_type < 2){
gain_type = 2;
}
} else {
while(gain > 1.0){
gain /= 1.5;
gain_type++;
}
if(gain_type > max_buckets){
gain_type = max_buckets - 1;
}
}
}
return gain_type;
}
//determines vertices to move out of oversized parts to satisfy balance constraint
//performs evictions before assigning destinations
//at most 14 kernels, 2 device-host syncs
vtx_view_t rebalance_strong(const problem& prob, const part_vt& part, const conn_data& cdata, scratch_mem& scratch, gain_vt part_sizes){
const matrix_t& g = prob.g;
const part_t k = prob.k;
const gain_t opt_size = prob.opt;
const wgt_view_t& vtx_w = prob.vtx_w;
ordinal_t n = g.numRows();
ordinal_t sections = max_sections;
ordinal_t section_size = (n + sections*k) / (sections*k);
if(section_size < 4096){
section_size = 4096;
sections = (n + section_size*k) / (section_size*k);
}
//use minibuckets within each gain bucket to reduce atomic contention
//because the number of gain buckets is small
ordinal_t t_minibuckets = max_buckets*k*sections;
vtx_view_t bucket_sizes = Kokkos::subview(scratch.vtx2, std::make_pair(static_cast<ordinal_t>(0), t_minibuckets + 2));
Kokkos::deep_copy(exec_space(), bucket_sizes, 0);
//atomically count vertices in each gain bucket
gain_t size_max = prob.size_max;
gain_t max_dest = std::min(opt_size + 1, prob.size_max);
gain_vt save_atomic = scratch.gain1;
gain_vt bid = scratch.gain2;
Kokkos::parallel_for("assign move scores part1", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i){
part_t p = part(i);
if(part_sizes(p) > size_max){
uint64_t tk = 0;
uint64_t tg = 0;
edge_offset_t start = cdata.conn_offsets(i);
part_t size = cdata.conn_table_sizes(i);
edge_offset_t end = start + size;
gain_t p_gain = 0;
//calculate average loss from moving to an adjacent part
for(edge_offset_t j = start; j < end; j++){
part_t pj = cdata.conn_entries(j);
if(pj == p){
p_gain = cdata.conn_vals(j);
} else if(pj > NULL_PART) {
if(part_sizes(pj) < max_dest){
tg += cdata.conn_vals(j);
tk += 1;
}
}
}
if(tk == 0) tk = 1;
gain_t gain = (tg / tk) - p_gain;
ordinal_t gain_type = gain_bucket(gain, vtx_w(i));
//add to count of appropriate bucket
if(gain_type < max_buckets && vtx_w(i) < 2*(part_sizes(p) - opt_size)){
ordinal_t g_id = (max_buckets*p + gain_type) * sections + (i % sections) + 1;
bid(i) = g_id;
save_atomic(i) = Kokkos::atomic_fetch_add(&bucket_sizes(g_id), 1);
} else {
save_atomic(i) = -1;
}
}
});
vtx_view_t bucket_offsets = bucket_sizes;
//scan bucket sizes to compute offsets
if(t_minibuckets < 10000 && !is_host_space){
Kokkos::parallel_for("scan scores", team_policy_t(1, 1024), KOKKOS_LAMBDA(const member& t){
//this scan is small so do it within a team instead of an entire grid to save kernel launch time
Kokkos::parallel_scan(Kokkos::TeamThreadRange(t, 0, t_minibuckets + 2), [&] (const ordinal_t i, ordinal_t& update, const bool final) {
ordinal_t curr = bucket_sizes(i);
if(final){
bucket_offsets(i) = update;
}
update += curr;
});
});
} else {
Kokkos::parallel_scan("scan scores", policy_t(0, t_minibuckets + 2), KOKKOS_LAMBDA(const ordinal_t& i, ordinal_t& update, const bool final){
ordinal_t curr = bucket_sizes(i);
if(final){
bucket_offsets(i) = update;
}
update += curr;
});
}
vtx_view_t least_bad_moves = scratch.vtx1;
Kokkos::parallel_for("assign move scores part2", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i){
part_t p = part(i);
if(part_sizes(p) > size_max){
ordinal_t insert = save_atomic(i);
if(insert > -1){
insert += bucket_offsets(bid(i));
least_bad_moves(insert) = i;
}
}
});
vtx_svt t_vtx_s = Kokkos::subview(bucket_offsets, t_minibuckets);
ordinal_t t_vtx = 0;
Kokkos::deep_copy(exec_space(), t_vtx, t_vtx_s);
least_bad_moves = Kokkos::subview(least_bad_moves, std::make_pair(static_cast<ordinal_t>(0), t_vtx));
gain_vt balance_scan = Kokkos::subview(scratch.gain1, std::make_pair(static_cast<ordinal_t>(0), t_vtx + 1));
//scan vwgts of possible moves after gathering into buckets
Kokkos::parallel_scan("assign move scores part3", policy_t(0, t_vtx), KOKKOS_LAMBDA(const ordinal_t i, gain_t& update, const bool final){
ordinal_t x = least_bad_moves(i);
update += vtx_w(x);
if(final){
balance_scan(i + 1) = update;
if(i == 0){
balance_scan(i) = 0;
}
}
});
gain_vt evict_start = scratch.evict_start;
gain_vt evict_end = scratch.evict_end;
Kokkos::parallel_for("find score cutoffs", policy_t(0, k), KOKKOS_LAMBDA(const int idx){
evict_start(idx) = bucket_offsets(idx*max_buckets*sections);
if(part_sizes(idx) > size_max){
gain_t evict_total = part_sizes(idx) - size_max;
ordinal_t start = bucket_offsets(idx*max_buckets*sections);
ordinal_t end = bucket_offsets((idx + 1)*max_buckets*sections);
gain_t find = balance_scan(start) + evict_total;
ordinal_t mid = (start + end) / 2;
//binary search to find eviction cutoffs for each k
while(start + 1 < end){
if(balance_scan(mid) >= find){
end = mid;
} else {
start = mid;
}
mid = (start + end) / 2;
}
//if(abs(balance_scan(end) - find) < abs(balance_scan(start) - find)){
evict_end(idx) = end;
//} else {
// evict_end(idx) = start;
//}
} else {
evict_end(idx) = bucket_offsets(idx*max_buckets*sections);
}
});
vtx_view_t moves = Kokkos::subview(scratch.vtx2, std::make_pair(static_cast<ordinal_t>(0), t_vtx));
ordinal_t num_moves = 0;
Kokkos::parallel_scan("filter below cutoffs", policy_t(0, t_vtx), KOKKOS_LAMBDA(const ordinal_t i, ordinal_t& update, const bool final){
ordinal_t u = least_bad_moves(i);
part_t p = part(u);
//vertices below cutoff are chosen for eviction
if(i < evict_end(p)){
if(final){
moves(update) = u;
}
update++;
}
}, num_moves);
t_vtx = num_moves;
vtx_view_t only_moves = Kokkos::subview(moves, std::make_pair(static_cast<ordinal_t>(0), t_vtx));
part_vt dest_part = scratch.dest_part;
vtx_view_t unassigned = only_moves;
//scan vwgts of evicted vertices
Kokkos::parallel_scan("balance scan", policy_t(0, t_vtx), KOKKOS_LAMBDA(const ordinal_t i, gain_t& update, const bool final){
ordinal_t x = unassigned(i);
update += vtx_w(x);
if(final){
balance_scan(i + 1) = update;
if(i == 0){
balance_scan(i) = 0;
}
}
});
//assign consecutive chunks of vertices to undersized parts using scan result
Kokkos::parallel_for("cookie cutter", policy_t(0, 1), KOKKOS_LAMBDA(const int idx){
if(idx == 0){
evict_start(0) = 0;
for(int p = 0; p < k; p++){
gain_t select = 0;
if(max_dest > part_sizes(p)){
select = max_dest - part_sizes(p);
}
ordinal_t start = evict_start(p);
ordinal_t end = t_vtx;
gain_t find = balance_scan(start) + select;
ordinal_t mid = (start + end) / 2;
//binary search to find eviction cutoffs for each k
while(start + 1 < end){
if(balance_scan(mid) >= find){
end = mid;
} else {
start = mid;
}
mid = (start + end) / 2;
}
if(abs(balance_scan(end) - find) < abs(balance_scan(start) - find)){
evict_end(p) = end;
} else {
evict_end(p) = start;
}
if(p + 1 < k){
evict_start(p+1) = evict_end(p);
}
}
}
});
Kokkos::parallel_for("select destination parts (rs)", policy_t(0, t_vtx), KOKKOS_LAMBDA(const ordinal_t i){
int p = 0;
//find chunk that contains i
while(p < k && evict_start(p) <= i){
p++;
}
p--;
if(i < evict_end(p)){
dest_part(unassigned(i)) = p;
} else {
dest_part(unassigned(i)) = part(unassigned(i));
}
});
return only_moves;
}
//determines vertices to move out of oversized parts to satisfy balance constraint
//performs evictions after assigning destinations
//at most 8 kernels, 1 device-host sync
vtx_view_t rebalance_weak(const problem& prob, const part_vt& part, const conn_data& cdata, scratch_mem& scratch, gain_vt part_sizes){
const matrix_t& g = prob.g;
const part_t k = prob.k;
const gain_t opt_size = prob.opt;
const wgt_view_t& vtx_w = prob.vtx_w;
ordinal_t n = g.numRows();
ordinal_t sections = max_sections;
ordinal_t section_size = (n + sections*k) / (sections*k);
if(section_size < 4096){
section_size = 4096;
sections = (n + section_size*k) / (section_size*k);
}
//use minibuckets within each gain bucket to reduce atomic contention
//because the number of gain buckets is small
ordinal_t t_minibuckets = max_buckets*k*sections;
gain_vt bucket_offsets = Kokkos::subview(scratch.gain1, std::make_pair(static_cast<ordinal_t>(0), t_minibuckets + 1));
gain_vt bucket_sizes = bucket_offsets;
Kokkos::deep_copy(exec_space(), bucket_sizes, 0);
part_vt dest_part = scratch.dest_part;
gain_t size_max = prob.size_max;
gain_vt save_gains = scratch.gain2;
part_vt undersized = scratch.undersized;
gain_t max_dest = size_max*0.99;
if(max_dest < size_max - 100){
max_dest = size_max - 100;
}
part_svt total_undersized = scratch.total_undersized;
Kokkos::parallel_for("init undersized parts list", team_policy_t(1, Kokkos::AUTO), KOKKOS_LAMBDA(const member& t){
//this scan is small so do it within a team instead of an entire grid to save kernel launch time
Kokkos::parallel_scan(Kokkos::TeamThreadRange(t, 0, k), [&] (const part_t i, part_t& update, const bool final) {
if(part_sizes(i) < max_dest){
if(final){
undersized(update) = i;
}
update++;
}
if(final && i + 1 == k){
total_undersized() = update;
}
});
});
Kokkos::parallel_for("select destination parts (rw)", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i) {
part_t p = part(i);
gain_t p_gain = 0;
part_t best = p;
gain_t gain = 0;
if(part_sizes(p) > size_max && vtx_w(i) < 1.5*(part_sizes(p) - opt_size)){
edge_offset_t start = cdata.conn_offsets(i);
part_t size = cdata.conn_table_sizes(i);
edge_offset_t end = start + size;
//find most connected undersized part
for(edge_offset_t j = start; j < end; j++){
part_t pj = cdata.conn_entries(j);
if(pj > NULL_PART && part_sizes(pj) < max_dest){
gain_t jgain = cdata.conn_vals(j);
if(jgain > gain){
best = pj;
gain = jgain;
}
}
if(pj == p){
p_gain = cdata.conn_vals(j);
}
}
if(gain > 0){
dest_part(i) = best;
save_gains(i) = gain - p_gain;
} else {
//choose arbitrary undersized part
best = undersized(i % total_undersized());
dest_part(i) = best;
save_gains(i) = -p_gain;
}
} else {
dest_part(i) = p;
}
});
gain_vt vscore = save_gains;
vtx_view_t bid = scratch.vtx2;
//atomically add vwgts in each gain bucket
//use atomic_fetch_add to get score
Kokkos::parallel_for("assign move scores", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i){
part_t p = part(i);
part_t best = dest_part(i);
bid(i) = -1;
if(p != best){
gain_t gain = save_gains(i);
ordinal_t gain_type = gain_bucket(gain, vtx_w(i));
ordinal_t g_id = (max_buckets*p + gain_type) * sections + (i % sections);
bid(i) = g_id;
vscore(i) = Kokkos::atomic_fetch_add(&bucket_sizes(g_id), vtx_w(i));
}
});
//exclusive prefix sum to compute offsets
//bucket_sizes is an alias of bucket_offsets
if(t_minibuckets < 10000 && !is_host_space){
Kokkos::parallel_for("scan score buckets", team_policy_t(1, 1024), KOKKOS_LAMBDA(const member& t){
//this scan is small so do it within a team instead of an entire grid to save kernel launch time
Kokkos::parallel_scan(Kokkos::TeamThreadRange(t, 0, t_minibuckets), [&] (const ordinal_t i, gain_t& update, const bool final) {
gain_t x = bucket_sizes(i);
if(final){
bucket_offsets(i) = update;
}
update += x;
});
});
} else {
Kokkos::parallel_scan("scan score buckets", policy_t(0, t_minibuckets), KOKKOS_LAMBDA(const ordinal_t& i, gain_t& update, const bool final){
gain_t x = bucket_sizes(i);
if(final){
bucket_offsets(i) = update;
}
update += x;
});
}
vtx_view_t moves = scratch.vtx1;
ordinal_t num_moves = 0;
Kokkos::parallel_scan("filter scores below cutoff", policy_t(0, n), KOKKOS_LAMBDA(const ordinal_t i, ordinal_t& update, const bool final){
ordinal_t b = bid(i);
if(b != -1){
part_t p = part(i);
ordinal_t begin_bucket = max_buckets*p*sections;
gain_t score = vscore(i) + bucket_offsets(b) - bucket_offsets(begin_bucket);
gain_t limit = part_sizes(p) - size_max;
if(score < limit){
if(final){
moves(update) = i;
}
update++;
}
}
}, num_moves);
vtx_view_t only_moves = Kokkos::subview(moves, std::make_pair(static_cast<ordinal_t>(0), num_moves));
return only_moves;
}
KOKKOS_INLINE_FUNCTION
static void build_row_cdata_large(const conn_data& cdata, const matrix_t& g, const part_vt part, const part_t k, const member& t){
ordinal_t i = t.league_rank();
edge_offset_t g_start = cdata.conn_offsets(i);
edge_offset_t g_end = cdata.conn_offsets(i + 1);
part_t size = g_end - g_start;
gain_t* s_conn_vals = (gain_t*) t.team_shmem().get_shmem(sizeof(gain_t) * size);
part_t* s_conn_entries = (part_t*) t.team_shmem().get_shmem(sizeof(part_t) * size);
part_t* used_cap = (part_t*) t.team_shmem().get_shmem(sizeof(part_t));
*used_cap = 0;
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
s_conn_vals[j] = 0;
});
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
s_conn_entries[j] = NULL_PART;
});
t.team_barrier();
//construct conn table in shared memory
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, g.graph.row_map(i), g.graph.row_map(i + 1)), [&] (const edge_offset_t& j){
ordinal_t v = g.graph.entries(j);
gain_t wgt = g.values(j);
part_t p = part(v);
part_t p_o = p % size;
if(size == k){
if(s_conn_entries[p_o] == NULL_PART && Kokkos::atomic_compare_exchange_strong(s_conn_entries + p_o, NULL_PART, p)) Kokkos::atomic_add(used_cap, 1);
} else {
bool success = false;
while(!success){
part_t px = s_conn_entries[p_o];
// the comparisons to p and NULL_PART need to be atomic
while(px != p && px != NULL_PART){
p_o = (p_o + 1) % size;
px = s_conn_entries[p_o];
}
if(px == p){
success = true;
} else {
//don't care if this thread succeeds if another thread succeeds with writing the same value
px = Kokkos::atomic_compare_exchange(s_conn_entries + p_o, NULL_PART, p);
if(px == NULL_PART){
px = p;
Kokkos::atomic_add(used_cap, 1);
}
if(px == p){
success = true;
} else {
p_o = (p_o + 1) % size;
}
}
}
}
Kokkos::atomic_add(s_conn_vals + p_o, wgt);
});
t.team_barrier();
part_t old_size = size;
size = *used_cap;
part_t quarter_size = size / 4;
part_t min_inc = 3;
if(quarter_size < min_inc) quarter_size = min_inc;
size += quarter_size;
if(size < old_size){
cdata.conn_table_sizes(i) = size;
//copy conn table into smaller conn table in global memory
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, old_size), [&] (const edge_offset_t& j){
part_t p = s_conn_entries[j];
if(p > NULL_PART){
part_t p_o = p % size;
bool success = false;
while(!success){
while(cdata.conn_entries(g_start + p_o) != NULL_PART){
p_o = (p_o + 1) % size;
}
if(Kokkos::atomic_compare_exchange_strong(&cdata.conn_entries(g_start + p_o), NULL_PART, p)){
success = true;
} else {
p_o = (p_o + 1) % size;
}
}
cdata.conn_vals(g_start + p_o) = s_conn_vals[j];
}
});
} else {
size = old_size;
cdata.conn_table_sizes(i) = size;
//copy conn table into global memory
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
cdata.conn_vals(g_start + j) = s_conn_vals[j];
});
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
cdata.conn_entries(g_start + j) = s_conn_entries[j];
});
}
}
//updates datastructures assuming a "large" number of vertices are moved
//2 kernels, 0 device-host syncs
void update_large(const problem& prob, part_vt part, const vtx_view_t swaps, scratch_mem& scratch, conn_data& cdata){
const matrix_t& g = prob.g;
const part_t k = prob.k;
ordinal_t total_moves = swaps.extent(0);
vtx_view_t swap_bit = scratch.zeros1;
Kokkos::parallel_for("mark adjacent", team_policy_t(total_moves, Kokkos::AUTO), KOKKOS_LAMBDA(const member& t){
ordinal_t i = swaps(t.league_rank());
//mark adjacent vertices
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, g.graph.row_map(i), g.graph.row_map(i + 1)), [=] (const edge_offset_t j){
ordinal_t v = g.graph.entries(j);
if(swap_bit(v) == 0) swap_bit(v) = 1;
});
});
//recompute conn tables for each vertex adjacent to a moved vertex
Kokkos::parallel_for("reset conn DS", team_policy_t(g.numRows(), Kokkos::AUTO).set_scratch_size(0, Kokkos::PerTeam(k*sizeof(gain_t) + k*sizeof(part_t) + 4*sizeof(part_t))), KOKKOS_LAMBDA(const member& t){
ordinal_t i = t.league_rank();
if(swap_bit(i) == 1){
edge_offset_t g_start = cdata.conn_offsets(i);
edge_offset_t g_end = cdata.conn_offsets(i + 1);
part_t size = g_end - g_start;
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
cdata.conn_vals(g_start + j) = 0;
});
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, 0, size), [&] (const edge_offset_t j) {
cdata.conn_entries(g_start + j) = NULL_PART;
});
build_row_cdata_large(cdata, g, part, k, t);
Kokkos::single(Kokkos::PerTeam(t), [=](){
//reset swap bit to 0 so memory can be reused
swap_bit(i) = 0;
cdata.dest_cache(i) = NULL_PART;
});
}
});
}
//update datastructures assuming a "small" number of vertices are moved
//2 kernels, 0 device-host syncs
void update_small(const problem& prob, const part_vt part, const vtx_view_t swaps, const part_vt dest_part, conn_data& cdata){
const matrix_t& g = prob.g;
const part_t k = prob.k;
ordinal_t total_moves = swaps.extent(0);
Kokkos::parallel_for("update conns (subtract) (high degree)", team_policy_t(total_moves, Kokkos::AUTO), KOKKOS_LAMBDA(const member& t){
ordinal_t i = swaps(t.league_rank());
//dest_part stores old part at this point
part_t p = dest_part(i);
//subtract i's contribution to p connectivity for adjacent vertices
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, g.graph.row_map(i), g.graph.row_map(i + 1)), [=] (const edge_offset_t j){
ordinal_t v = g.graph.entries(j);
gain_t wgt = g.values(j);
edge_offset_t v_start = cdata.conn_offsets(v);
part_t v_size = cdata.conn_table_sizes(v);
part_t p_o = p % v_size;
//v is always adjacent to p because it is adjacent to i which was in p
while(cdata.conn_entries(v_start + p_o) != p){
p_o = (p_o + 1) % v_size;
}
//DO NOT USE ATOMIC_ADD_FETCH HERE IT IS WAY SLOWER
gain_t x = Kokkos::atomic_fetch_add(&cdata.conn_vals(v_start + p_o), -wgt);
//parts have locked locations if v_size == k (even when not originally allocated to size k)
if(v_size < k && x == wgt){
//free this gain slot
cdata.conn_entries(v_start + p_o) = HASH_RECLAIM;
}
});
});
Kokkos::parallel_for("update conns (add) (high degree)", team_policy_t(total_moves, Kokkos::AUTO), KOKKOS_LAMBDA(const member& t){
ordinal_t i = swaps(t.league_rank());
//part contains new part at this point
part_t best = part(i);
//add i's contribution to best connectivity for adjacent vertices
Kokkos::parallel_for(Kokkos::TeamThreadRange(t, g.graph.row_map(i), g.graph.row_map(i + 1)), [=] (const edge_offset_t j){
ordinal_t v = g.graph.entries(j);
gain_t wgt = g.values(j);
cdata.dest_cache(v) = NULL_PART;
edge_offset_t v_start = cdata.conn_offsets(v);
part_t v_size = cdata.conn_table_sizes(v);
part_t p_o = best % v_size;
bool success = false;
//check if best in conn table
//can only determine best is absent if NULL_PART is found or v_size reached
for(part_t q = 0; q < v_size; q++){
part_t p_i = (best + q) % v_size;
if(cdata.conn_entries(v_start + p_i) == best){
success = true;
p_o = p_i;
break;
} else if(cdata.conn_entries(v_start + p_i) == NULL_PART){
break;
}
}
part_t count = 0;
//insert best into conn table
//needs to find either HASH_RECLAIM or NULL_PART to make insertion
while(!success && count < v_size){
part_t px = cdata.conn_entries(v_start + p_o);
// comparisons to best and NULL_PART need to be atomic
while(px != best && px > NULL_PART && count++ < v_size){
p_o = (p_o + 1) % v_size;
px = cdata.conn_entries(v_start + p_o);
}
if(px == best){
success = true;
} else if(px <= NULL_PART){
//don't care if this thread succeeds if another thread succeeds with writing the same value
px = Kokkos::atomic_compare_exchange(&cdata.conn_entries(v_start + p_o), px, best);
if(px == best || px <= NULL_PART){
success = true;
} else {
p_o = (p_o + 1) % v_size;
count++;
}
}
}
//if we run out of space, start densely allocating after end of current hash table
//this has the side-effect of making future lookups in this row O(v_size)
if(!success){
p_o = v_size;
while(!success){
part_t px = cdata.conn_entries(v_start + p_o);
// comparisons to best and NULL_PART need to be atomic
while(px != best && px > NULL_PART){
p_o++;
px = cdata.conn_entries(v_start + p_o);
}
if(px == best){
success = true;
} else {
//don't care if this thread succeeded if another thread succeeded with writing the same value
part_t py = Kokkos::atomic_compare_exchange(&cdata.conn_entries(v_start + p_o), px, best);
if(py == px){
py = best;
Kokkos::atomic_add(&cdata.conn_table_sizes(v), 1);
}
if(py == best){
success = true;
} else {
p_o++;
}
}
}
}
Kokkos::atomic_add(&cdata.conn_vals(v_start + p_o), wgt);
});
});
}
KOKKOS_INLINE_FUNCTION
static gain_t lookup(const part_t* keys, const gain_t* vals, const part_t& target, const part_t& size){
for(part_t q = 0; q < size; q++){
part_t p_i = (target + q) % size;
if(keys[p_i] == target){
return vals[p_i];
} else if(keys[p_i] == NULL_PART){
return 0;
}
}
return 0;
}
//perform swaps, update gains, and compute change to cut and imbalance
//4 kernels, 1 device-host syncs
void perform_moves(const problem& prob, part_vt part, const vtx_view_t swaps, const part_vt dest_part, scratch_mem& scratch, conn_data cdata, refine_data& curr_state){
const matrix_t& g = prob.g;
const wgt_view_t& vtx_w = prob.vtx_w;
ordinal_t total_moves = swaps.extent(0);
//total change in cutsize = (sum over all moves) -((new_b_con - new_p_con) + (old_b_con - old_p_con))
Kokkos::parallel_reduce("count cutsize change part1", policy_t(0, total_moves), KOKKOS_LAMBDA(const ordinal_t& x, gain_t& gain_update){
ordinal_t i = swaps(x);
part_t best = dest_part(i);
part_t p = part(i);
edge_offset_t start = cdata.conn_offsets(i);
part_t size = cdata.conn_table_sizes(i);
gain_t p_con = lookup(cdata.conn_entries.data() + start, cdata.conn_vals.data() + start, p, size);
gain_t b_con = lookup(cdata.conn_entries.data() + start, cdata.conn_vals.data() + start, best, size);
gain_update += b_con - p_con;
}, scratch.cut_change1);
//change part assignments and update part sizes
Kokkos::parallel_for("perform moves", policy_t(0, total_moves), KOKKOS_LAMBDA(const ordinal_t x){
ordinal_t i = swaps(x);
part_t p = part(i);
part_t best = dest_part(i);
cdata.dest_cache(i) = NULL_PART;
Kokkos::atomic_add(&curr_state.part_sizes(p), -vtx_w(i));
Kokkos::atomic_add(&curr_state.part_sizes(best), vtx_w(i));
part(i) = best;
//update needs to know old part assignment
dest_part(i) = p;
});
if(total_moves > static_cast<ordinal_t>(g.numRows() / 10)){
update_large(prob, part, swaps, scratch, cdata);
} else {
update_small(prob, part, swaps, dest_part, cdata);
}
Kokkos::parallel_reduce("count cutsize change part2", policy_t(0, total_moves), KOKKOS_LAMBDA(const ordinal_t& x, gain_t& gain_update){
ordinal_t i = swaps(x);
part_t p = dest_part(i);
part_t best = part(i);
edge_offset_t start = cdata.conn_offsets(i);