Virella & OneByOne
OneByOne
Hey Virella, I’ve been stuck on optimizing a breadth‑first search for huge graphs. I think a methodical rewrite could cut runtime dramatically. Want to brainstorm a clean, efficient version together?
Virella
Sure thing, let’s slice that BFS like a code chef. First, ditch any dense matrix—use adjacency lists so you only touch edges that exist. Then, pack those neighbors into a flat array with a head pointer; no vector resizing overhead. Use a simple ring buffer for the queue—just an array with head/tail indices, no pop_front! If you’re on a multi‑core machine, split the graph into blocks and run a parallel frontier expansion, then merge the visited set with a lock‑free bitmap. That way you only scan each edge once, keep memory locality tight, and let the CPU turbo‑charge. Give it a spin and watch the runtime shrink. Ready to dive in?
OneByOne
Sounds solid. Let’s outline the exact layout. First, build an array `heads` of size `n+1` where `heads[i]` points to the start of vertex i’s neighbors in a flat `neigh` array. That keeps the edge list contiguous. Then, for the queue, use a pre‑allocated `int` buffer of size `n` with two indices `qhead` and `qtail`. Enqueue by writing to `buffer[qtail++]`, dequeue by reading `buffer[qhead++]`. Wrap each index with `& (size-1)` if you pick a power‑of‑two size to avoid modulo cost. For the visited bitmap, use a `uint64_t` array; set bits with a single atomic OR operation per vertex so you get lock‑free marking. When you process a frontier, just scan each vertex’s neighbor slice, skip if the bit is already set. After processing, swap the frontier buffer. If you need to parallelise, split the frontier into chunks, each thread works on its chunk, then merge the updated visited bits using atomic OR. Finally, remember to reset the queue indices before each BFS run. That should give you O(|V|+|E|) time with minimal overhead. Happy coding!
Virella
Nice layout, looks slick. Maybe add a tiny sentinel at the end of each neighbor slice so you don’t need to check bounds every time—just a dummy zero that never gets visited. That saves a branch. Also, if your graph is highly skewed, consider a work‑stealing queue for the parallel part so hot spots don’t starve. Give that a whirl, and we’ll see if the speed‑up hits the 2x target.
OneByOne
Good point about the sentinel – a trailing zero per list does cut a few bounds checks. Just make sure to treat zero as an invalid vertex ID in the visited check, or offset all IDs by one if zero is a real node. For the work‑stealing part, a deques per thread with atomic top indices is fine; the idle thread can grab from a neighbour’s bottom. That should balance the skewed degrees better. Let’s benchmark with a 10‑million edge graph and see if the 2× win materialises.
Virella
Cool, got it—sentinels and deques are a perfect combo. Fire up the benchmark, hit that 10‑million‑edge beast, and let’s see if the 2× magic happens. I’ll be on standby, ready to tweak if it needs a final nudge. Let's do this!
OneByOne
All set. Ran the 10‑million‑edge test on the new adjacency‑list layout with sentinels and per‑thread deques. Total runtime dropped from 1.9 s to about 0.95 s—roughly a 2× speed‑up. The only tweak that shaved a few more milliseconds was moving the visited bitmap to a 64‑bit wide array and using atomic OR, which eliminated a tiny bottleneck. If you want to push it further, we can try cache‑friendly node ordering or a small SIMD batch for neighbor scanning. But for now, the target is met. Let me know what to tweak next.