Request to share information regarding deadlock in postgresql-8.1.18

Dear All,

Thanks in advance.

In my Linux system, below error is found and after 10~12 hours, WAL file in pg_xlog directory are increased
continuously.
PostgreSQL:ERROR:  deadlock detected
DETAIL:  Process 12345 waits for AccessShareLock on relation 16446 of database 16385; blocked by process 23136.
Process 23136 waits for ShareLock on relation 16482 of database 16385; blocked by process 12345.
CONTEXT:  SQL statement "SELECT 1 FROM ONLY "public"."table name" x WHERE "id" = $1 AND "table_id" = $2 FOR SHARE OF
x"

Is this deadlock error is link with WAL file of pg_xlog?
Please share your opinion. 

Regards,
Yogesh