On the Hardness of Approximating the Min-Hack Problem
نویسندگان
چکیده
We study the hardness of approximation for the MINIMUM HACKING problem, which roughly can be described as the problem of finding the best way to compromise some target nodes given a few initial compromised nodes in a network. We give three reductions to show that MINIMUM HACKING is not approximable to within where , for any ! " $#% . In particular, the reductions are from a PCP, from the MINIMUM LABEL COVER problem, and from the MINIMUM MONOTONE SATISFYING ASSIGNMENT problem. We also analyze some heuristics on this problem.
منابع مشابه
On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem
We study hardness of approximating several minimaximal and maximinimal NP-optimization problems related to the minimum linear ordering problem (MINLOP). MINLOP is to find a minimum weight acyclic tournament in a given arc-weighted complete digraph. MINLOP is APX-hard but its unweighted version is polynomial time solvable. We prove that, MIN-MAX-SUBDAG problem, which is a generalization of MINLO...
متن کاملStrengthened Hardness for Approximating Minimum Unique Game and Small Set Expansion
In this paper, the author puts forward a variation of Feige’s Hypothesis, which claims that it is hard on average refuting Unbalanced Max 3-XOR against biased assignments on a natural distribution. Under this hypothesis, the author strengthens the previous known hardness for approximating Minimum Unique Game, 5/4 − ǫ, by proving that Min 2-Lin-2 is hard to within 3/2 − ǫ and strengthens the pre...
متن کاملInapproximability of Minimum Vertex Cover
Last time we examined a generic approach for inapproximability results based on the Unique Games Conjecture. Before, we had already shown that approximating MAX-3-LIN to within a constant factor larger than 12 is NP-hard. To do this we used a tweaked version of our dictatorship test that we came up with earlier in the semester. Last time we (re)proved that approximating MAX-3-LIN to within a co...
متن کاملMin-Rep instances with large supergirth and the hardness of approximating basic spanners
We study the Min-rep with large supergirth problem. We show that if the supergirth in the Min-Rep graph is some k, 0 < k ≤ log1−2ǫ n, the problem is roughly 2log 1−ǫ n/k hard to approximate. A similar theorem was claimed by the paper [19] from ICALP 2000. However their paper contains an error. We use the new proof to show inapproximability for the min-size k-spanner problem which is the simples...
متن کاملApproximating the Minmax Value of Three-Player Games within a Constant is as Hard as Detecting Planted Cliques
We consider the problem of approximating the minmax value of a multiplayer game in strategic form. We argue that in 3-player games with 0-1 payoffs, approximating the minmax value within an additive constant smaller than ξ/2, where ξ = 3− √ 5 2 ≈ 0.382, is not possible by a polynomial time algorithm. This is based on assuming hardness of a version of the socalled planted clique problem in Erdős...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Optim.
دوره 9 شماره
صفحات -
تاریخ انتشار 2005