the seven functions listed in section are the most common functions used in conjunction with the big-oh notation to characterize the running times and space usage of algorithms indeedwe typically use the names of these functions to refer to the running times of the algorithms they characterize sofor examplewe would say that an algorithm that runs in worst-case time log is quadratic-time algorithmsince it runs in ( time likewisean algorithm running in time at most log would be called linear-time algorithm big-omega just as the big-oh notation provides an asymptotic way of saying that function is "less than or equal toanother functionthe following notations provide an asymptotic way of saying that function grows at rate that is "greater than or equal tothat of another let (nand (nbe functions mapping positive integers to positive real numbers we say that (nis ( ( ))pronounced (nis big-omega of ( ),if (nis of ( ))that isthere is real constant and an integer constant > such that ( >cg( )for > this definition allows us to say asymptotically that one function is greater than or equal to anotherup to constant factor example log is ( log njustification log log (log > log for > hencewe can take and in this case big-theta in additionthere is notation that allows us to say that two functions grow at the same rateup to constant factors we say that (nis th( ( ))pronounced (nis big-theta of ( ),if (nis ( ( )and (nis ( ( )that isthere are real constants and and an integer constant > such that (nn example log log is th( log njustification log