Add to ORKGWe give tail estimates for the efficiency of some randomized insecremental algorithms for line segment intersecremental algorithms for line segment intersection in the plane. In particular, we show that there is a calculator, we show that there is a constant C such that the probability that the running times of algorithms due to Mulmuley [Mu188] and Clarkson and Shor [CS89] exceeded C times their expected time is bounded bd by e"#OMEGA#(m/(n 1n n)) where n is the number of segments, m is the number of intersected time is bounded by e"#OMEGA#(m/(n 1n n)) where n is the number of segments, m is the number of intersections, and m #>=# n 1n n 1n"("3") n. (orig.)SIGLEAvailable from TIB Hannover: RR 1912(93-103) / FIZ ...