netdev - Re: [PATCH v3 net-next 11/14] af_unix: Assign a unique index to SCC.

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Date: Tue, 27 Feb 2024 12:19:40 +0100
From: Paolo Abeni <pabeni@...hat.com>
To: Kuniyuki Iwashima <kuniyu@...zon.com>, "David S. Miller"
	 <davem@...emloft.net>, Eric Dumazet <edumazet@...gle.com>, Jakub Kicinski
	 <kuba@...nel.org>
Cc: Kuniyuki Iwashima <kuni1840@...il.com>, netdev@...r.kernel.org
Subject: Re: [PATCH v3 net-next 11/14] af_unix: Assign a unique index to SCC.

On Fri, 2024-02-23 at 13:40 -0800, Kuniyuki Iwashima wrote:
> The definition of the lowlink in Tarjan's algorithm is the
> smallest index of a vertex that is reachable with at most one
> back-edge in SCC.  This is not useful for a cross-edge.
> 
> If we start traversing from A in the following graph, the final
> lowlink of D is 3.  The cross-edge here is one between D and C.
> 
>   A -> B -> D   D = (4, 3)  (index, lowlink)
>   ^    |    |   C = (3, 1)
>   |    V    |   B = (2, 1)
>   `--- C <--'   A = (1, 1)
> 
> This is because the lowlink of D is updated with the index of C.
> 
> In the following patch, we detect a dead SCC by checking two
> conditions for each vertex.
> 
>   1) vertex has no edge directed to another SCC (no bridge)
>   2) vertex's out_degree is the same as the refcount of its file
> 
> If 1) is false, there is a receiver of all fds of the SCC and
> its ancestor SCC.
> 
> To evaluate 1), we need to assign a unique index to each SCC and
> assign it to all vertices in the SCC.
> 
> This patch changes the lowlink update logic for cross-edge so
> that in the example above, the lowlink of D is updated with the
> lowlink of C.
> 
>   A -> B -> D   D = (4, 1)  (index, lowlink)
>   ^    |    |   C = (3, 1)
>   |    V    |   B = (2, 1)
>   `--- C <--'   A = (1, 1)
> 
> Then, all vertices in the same SCC have the same lowlink, and we
> can quickly find the bridge connecting to different SCC if exists.
> 
> However, it is no longer called lowlink, so we rename it to
> scc_index.  (It's sometimes called lowpoint.)
> 
> Also, we add a global variable to hold the last index used in DFS
> so that we do not reset the initial index in each DFS.
> 
> This patch can be squashed to the SCC detection patch but is
> split deliberately for anyone wondering why lowlink is not used
> as used in the original Tarjan's algorithm and many reference
> implementations.
> 
> Signed-off-by: Kuniyuki Iwashima <kuniyu@...zon.com>
> ---
>  include/net/af_unix.h |  2 +-
>  net/unix/garbage.c    | 15 ++++++++-------
>  2 files changed, 9 insertions(+), 8 deletions(-)
> 
> diff --git a/include/net/af_unix.h b/include/net/af_unix.h
> index ec040caaa4b5..696d997a5ac9 100644
> --- a/include/net/af_unix.h
> +++ b/include/net/af_unix.h
> @@ -36,7 +36,7 @@ struct unix_vertex {
>  	struct list_head scc_entry;
>  	unsigned long out_degree;
>  	unsigned long index;
> -	unsigned long lowlink;
> +	unsigned long scc_index;
>  };
>  
>  struct unix_edge {
> diff --git a/net/unix/garbage.c b/net/unix/garbage.c
> index 1d9a0498dec5..0eb1610c96d7 100644
> --- a/net/unix/garbage.c
> +++ b/net/unix/garbage.c
> @@ -308,18 +308,18 @@ static bool unix_scc_cyclic(struct list_head *scc)
>  
>  static LIST_HEAD(unix_visited_vertices);
>  static unsigned long unix_vertex_grouped_index = UNIX_VERTEX_INDEX_MARK2;
> +static unsigned long unix_vertex_last_index = UNIX_VERTEX_INDEX_START;
>  
>  static void __unix_walk_scc(struct unix_vertex *vertex)
>  {
> -	unsigned long index = UNIX_VERTEX_INDEX_START;
>  	LIST_HEAD(vertex_stack);
>  	struct unix_edge *edge;
>  	LIST_HEAD(edge_stack);
>  
>  next_vertex:
> -	vertex->index = index;
> -	vertex->lowlink = index;
> -	index++;
> +	vertex->index = unix_vertex_last_index;
> +	vertex->scc_index = unix_vertex_last_index;
> +	unix_vertex_last_index++;
>  
>  	list_add(&vertex->scc_entry, &vertex_stack);
>  
> @@ -342,13 +342,13 @@ static void __unix_walk_scc(struct unix_vertex *vertex)
>  
>  			vertex = edge->predecessor->vertex;
>  
> -			vertex->lowlink = min(vertex->lowlink, next_vertex->lowlink);
> +			vertex->scc_index = min(vertex->scc_index, next_vertex->scc_index);
>  		} else if (next_vertex->index != unix_vertex_grouped_index) {
> -			vertex->lowlink = min(vertex->lowlink, next_vertex->index);
> +			vertex->scc_index = min(vertex->scc_index, next_vertex->scc_index);

I guess the above will break when unix_vertex_last_index wraps around,
or am I low on coffee? (I guess there is not such a thing as enough
coffee to allow me reviewing this whole series at once ;)

Can we expect a wrap around in host with (surprisingly very) long
uptimes? 

Thanks,

Paolo