int OptimalOverlapping::constraints(var_env *e, gurobi_ctx *ctx, QueryWorkload const * workload, common::SchemaStats const & stats)
{
int error = 0;
int j = 0;
std::vector<QuerySummary> const & queries = workload->getQuerySummaries();
/* First set of constraints */
for (int a = 0; a < e->A; ++a) {
j = 0;
for (int p = 0; p < e->P; ++p) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = 1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->P, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 1.0, NULL);
if (error) return error;
}
/* Second set of constraints */
for (int a = 0; a < e->A; ++a) {
for (int q = 0; q < e->Q; ++q) {
j = 0;
for (int p = 0; p < e->P; ++p) {
ctx->ind[j] = z(e,a,p,q);
ctx->val[j] = 1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->P, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, accesses(queries,q,a), NULL);
if (error) return error;
}
}
/* Third set of constraints */
for (int a = 0; a < e->A; ++a) {
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
ctx->ind[0] = x(e,a,p);
ctx->val[0] = 1.0;
ctx->ind[1] = z(e,a,p,q);
ctx->val[1] = -1.0;
error = GRBaddconstr(ctx->model, 2, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
}
}
/* Fourth set of constraints */
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
j = 0;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = z(e,a,p,q);
ctx->val[j] = 1.0;
j++;
}
ctx->ind[j] = y(e,p,q);
ctx->val[j] = -1.0;
error = GRBaddconstr(ctx->model, e->A + 1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
}
/* Fifth set of constraints */
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
j = 0;
ctx->ind[j] = y(e,p,q);
ctx->val[j] = K();
j++;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = z(e,a,p,q);
ctx->val[j] = -1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->A + 1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
}
/* 6th set of constraints */
for (int a = 0; a < e->A; ++a) {
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
ctx->ind[0] = z(e,a,p,q);
ctx->val[0] = 1.0;
ctx->ind[1] = x(e,a,p);
ctx->val[1] = -1.0;
ctx->ind[2] = y(e,p,q);
ctx->val[2] = -1.0;
error = GRBaddconstr(ctx->model, 3, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, -1.0, NULL);
if (error) return error;
}
}
}
/* 7th set of constraints */
for (int p = 0; p < e->P; ++p) {
j = 0;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = 1.0;
j++;
}
ctx->ind[j] = u(e,p);
ctx->val[j] = -1.0;
error = GRBaddconstr(ctx->model, e->A+1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
/* 8th set of constraints */
for (int p = 0; p < e->P; ++p) {
j = 0;
ctx->ind[j] = u(e,p);
ctx->val[j] = K();
j++;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = -1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->A+1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
auto const & attributes = workload->getAttributes();
Cost cost(stats);
Partition part;
for_each(attributes.begin(), attributes.end(), [&] (Attribute const * attr) {
part.addAttribute(attr);
});
double limit = cost.getPartitionSize(part) * (1 + alpha());
double u_const =
(SystemConstants::edgeIdSize + SystemConstants::timestampSize) * c_e()
+ (SystemConstants::headVertexSize + SystemConstants::numEntriesSize) * c_n();
/* 9th set of constraints */
j = 0;
for (int p = 0; p < e->P; ++p) {
ctx->ind[j] = u(e,p);
ctx->val[j] = u_const;
j++;
}
for (int p = 0; p < e->P; ++p) {
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = stats.getAvgSize(workload->getAttribute(a).getIndex()) * c_e();
j++;
}
}
error = GRBaddconstr(ctx->model, e->P + e->P*e->A, ctx->ind, ctx->val,
GRB_LESS_EQUAL, limit, NULL);
if (error) return error;
error = GRBupdatemodel(ctx->model);
if (error) return error;
return error;
}
int OptimalNonOverlapping::constraints(var_env *e, gurobi_ctx *ctx, QueryWorkload const * workload, common::SchemaStats const & stats)
{
int error = 0;
int j = 0;
std::vector<QuerySummary> const & queries = workload->getQuerySummaries();
/* First set of constraints */
for (int a = 0; a < e->A; ++a) {
j = 0;
for (int p = 0; p < e->P; ++p) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = 1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->P, ctx->ind, ctx->val,
GRB_EQUAL, 1.0, NULL);
if (error) return error;
}
/* Second set of constraints */
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
j = 0;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = accesses(queries,q,a);
j++;
}
ctx->ind[j] = y(e,p,q);
ctx->val[j] = -1.0;
error = GRBaddconstr(ctx->model, e->A + 1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
}
/* Third set of constraints */
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
j = 0;
ctx->ind[j] = y(e,p,q);
ctx->val[j] = K();
j++;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = -(accesses(queries,q,a));
j++;
}
error = GRBaddconstr(ctx->model, e->A + 1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
}
/* Fourth set of constraints */
for (int a = 0; a < e->A; ++a) {
for (int p = 0; p < e->P; ++p) {
for (int q = 0; q < e->Q; ++q) {
ctx->ind[0] = z(e,a,p,q);
ctx->val[0] = 1.0;
ctx->ind[1] = x(e,a,p);
ctx->val[1] = -1.0;
ctx->ind[2] = y(e,p,q);
ctx->val[2] = -1.0;
error = GRBaddconstr(ctx->model, 3, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, -1.0, NULL);
if (error) return error;
}
}
}
/* Fifth set of constraints */
for (int p = 0; p < e->P; ++p) {
j = 0;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = 1.0;
j++;
}
ctx->ind[j] = u(e,p);
ctx->val[j] = -1.0;
error = GRBaddconstr(ctx->model, e->A+1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
/* Sixth set of constraints */
for (int p = 0; p < e->P; ++p) {
j = 0;
ctx->ind[j] = u(e,p);
ctx->val[j] = K();
j++;
for (int a = 0; a < e->A; ++a) {
ctx->ind[j] = x(e,a,p);
ctx->val[j] = -1.0;
j++;
}
error = GRBaddconstr(ctx->model, e->A+1, ctx->ind, ctx->val,
GRB_GREATER_EQUAL, 0.0, NULL);
if (error) return error;
}
auto const & attributes = workload->getAttributes();
Cost cost(stats);
Partition part;
for_each(attributes.begin(), attributes.end(), [&] (Attribute const * attr) {
part.addAttribute(attr);
});
double limit = 1.0 + alpha() / (1.0 - (s(workload->getAttributes(), stats) * c_e()) / cost.getPartitionSize(part));
/* 6th set of constraints */
j = 0;
for (int p = 0; p < e->P; ++p) {
int index = u(e,p);
ctx->ind[j] = index;
ctx->val[j] = 1;
j++;
}
error = GRBaddconstr(ctx->model, e->P, ctx->ind, ctx->val,
GRB_LESS_EQUAL, limit, NULL);
if (error) return error;
error = GRBupdatemodel(ctx->model);
if (error) return error;
return error;
}