منابع مشابه
Note on Max Lin-2 above Average
In the Max Lin-2 problem we are given a system S of m linear equations in n variables over F2 in which Equation j is assigned a positive integral weight wj for each j. We wish to find an assignment of values to the variables which maximizes the total weight of satisfied equations. This problem generalizes Max Cut. The expected weight of satisfied equations is W/2, where W = w1 + · · ·+ wm; W/2 ...
متن کاملNote on MAX 2SAT
In this note we present an approximation algorithm for MAX 2SAT that given a (1− ε) satisfiable instance finds an assignment of variables satisfying a 1−O( √ ε) fraction of all constraints. This result is optimal assuming the Unique Games Conjecture. The best previously known result, due to Zwick, was 1−O(ε1/3). We believe that the analysis of our algorithm is much simpler than the analysis of ...
متن کاملSolving MAX-2-SAT Above a Tight Lower Bound
We present an exact algorithm that decides in time m + 2 ) whether a given set of m binary clauses admits a truth assignment that satisfies at least (3m + k)/4 clauses. Thus Max-2-Sat is fixed-parameter tractable when parameterized above the tight lower bound 3m/4. Our algorithm is based on a polynomial-time data reduction procedure that reduces a problem instance to an equivalent one with O(k)...
متن کاملNew Upper Bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the Average Variable Degree
MAX-2-SAT and MAX-2-CSP are important NP-hard optimization problems generalizing many graph problems. Despite many efforts, the only known algorithm (due to Williams) solving them in less than 2 steps uses exponential space. Scott and Sorkin give an algorithm with 2 2 d+1 ) time and polynomial space for these problems, where d is the average variable degree. We improve this bound to O∗(2 10/3 d...
متن کاملSimultaneously Satisfying Linear Equations Over $\mathbb{F}_2$: MaxLin2 and Max-$r$-Lin2 Parameterized Above Average
In the parameterized problem MAXLIN2-AA[k], we are given a system with variables x1, . . . , xn consisting of equations of the form ∏ i∈I xi = b, where xi, b ∈ {−1, 1} and I ⊆ [n], each equation has a positive integral weight, and we are to decide whether it is possible to simultaneously satisfy equations of total weight at least W/2+ k, where W is the total weight of all equations and k is the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2010
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2010.04.010