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The compact attack graphs implicitly reveal the threat of sophisticated multi-step attacks by enumerating possible sequences of exploits leading to the compromising given critical resources in enterprise networks with thousands of hosts. For security analysts, the challenge is how to analyze the complex attack graphs with possible ten thousands of nodes for defending the security of network. In the paper, we will essentially discuss two issues about it. The first is to compute non-loop attack paths with the distance less than the given number that the real attacker may take practically in realistic attack scenarios. The second is to find the solution to removing vulnerabilities in such a way that given critical resources cannot be compromised while the cost for such removal incurs the least cost. We propose two scalable approaches to solve the above two issues respectively. These two approaches are proved to have a polynomial time complexity and can scale to the attack graphs with ten thousands of nodes corresponding large enterprise networks.