The polynomial time algorithm of 2-SAT involving SCC tells us whether a solution exists or not and also helps us in generating a solution to the problem . But there can be more than one solution . I wanted to know is it possible to generate other solutions efficiently using the existing one ?
Generation solutions to 2-SAT from an existing one
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I guess it depends on your definition of "other solutions", for example the optimization problem of 2SAT (solution with minimal number of variables as 1s), is NP-Complete.
If you want any solution, and by "efficient" you mean polynomial time - you can flip variables in your assignment from true->false and vise versa (one simple way to do it is adding
(x OR x)or for false(^x OR ^x)as a clause). Then, rerunning your 2SAT solver will give you a different solution, if such exist. You need to rerun your 2SAT solver at mostntimes, wherenis the number of variables, and since your 2SAT solver is also polynomial time, this solution runs in polynomial time.