DoS and DDoS attacks are widely used and pose a constant threat. Here we explore Probability Packet Marking (PPM), one of the important methods for reconstructing the attack-graph and detect the attackers. We present two algorithms. Differently from others, their stopping time is not fixed a priori. It rather depends on the actual distance of the attacker from the victim. Our first algorithm returns the graph at the earliest feasible time, and turns out to guarantee high success probability. The second algorithm enables attaining any predetermined success probability at the expense of a longer runtime. We study the performance of the two algorithms theoretically, and compare them to other algorithms by simulation. Finally, we consider the order in which the marks corresponding to the various edges of the attack graph are obtained by the victim. We show that, although edges closer to the victim tend to be discovered earlier in the process than farther edges, the differences are much smaller than previously thought.