Melkij

with vertex_cost as (
select fid_id, sum(vertex_cost) as vertex_cost /*min, max аналогично*/ from vertex group by fid_id
),
edge_cost as (
select fid_id, sum(edge_cost) as edge_cost /*min, max*/ from edge group by fid_id
)
select id, name, vertex_cost, edge_cost
    from fig
    left join vertex_cost vc on fig.id=vc.fig_id
    left join edge_cost ec on fig.id=ec.fig_id

with figures as (
select id, name from figures where name like 'foo%'
),
vertex_cost as (
select fid_id, sum(vertex_cost) as vertex_cost /*min, max*/ from vertex where fig_id in (select id from figures) group by fid_id
),
edge_cost as (
select fid_id, sum(edge_cost) as edge_cost /*min, max*/ from edge where fig_id in (select id from figures) group by fid_id
)
select id, name, vertex_cost, edge_cost
    from figures
    left join vertex_cost vc on figures.id=vc.fig_id
    left join edge_cost ec on figures.id=ec.fig_id

All constraints on all partitions of the master table are examined during constraint exclusion, so large numbers of partitions are likely to increase query planning time considerably. Partitioning using these techniques will work well with up to perhaps a hundred partitions; don't try to use many thousands of partitions.