Results 1  10
of
16
2CNF Deletion [1].
"... Definition 1 (Min UnCut Problem) Given a graph G =(V,E), find a cut that minimizes the number of uncut edges i.e. the number of edges within each part. Remark 1 The Min UnCut problem is a complement to the MaxCut problem: The sum of the number of cut edges and uncut edges is equal to the total numbe ..."
Abstract
 Add to MetaCart
∈ S ′ : i ≥ 0}; T = {i ∈ T ′ : i ≥ 0}. Thus Min UnCut is equivalent to the following problem: Definition 2 Given a graph G =(V,E), where V = {−n,...,−1} ∪{−1,...,−n} findacut (S, T = −S) that minimizes the number of cut edges i.e. the number of edges going from the part S to T. 1.1 SDP relaxation Write
On the Hardness of Approximating Multicut and SparsestCut
 In Proceedings of the 20th Annual IEEE Conference on Computational Complexity
, 2005
"... We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1. ..."
Abstract

Cited by 102 (5 self)
 Add to MetaCart
We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1.
Abstract
, 2004
"... We show that the MULTICUT, SPARSESTCUT and MIN2CNF £ DELETION problems are hard to approximate, assuming the Unique Games Conjecture of Khot [Kho02]. In particular, we obtain an arbitrarily large constant factor hardness for these problems, and show that a quantitatively stronger version of the co ..."
Abstract
 Add to MetaCart
We show that the MULTICUT, SPARSESTCUT and MIN2CNF £ DELETION problems are hard to approximate, assuming the Unique Games Conjecture of Khot [Kho02]. In particular, we obtain an arbitrarily large constant factor hardness for these problems, and show that a quantitatively stronger version
Almost 2SAT is fixedparameter tractable
 Journal of Computer and System Sciences
"... Abstract. We consider the following problem. Given a 2CNF formula, is it possible to remove at most k clauses so that the resulting 2CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer Science under the names ’Almost 2SAT’, ’Allbutk 2SAT’ ..."
Abstract

Cited by 40 (5 self)
 Add to MetaCart
’, ’2CNF deletion’, ’2SAT deletion’. The status of fixedparameter tractability of this problem is a longstanding open question in the area of Parameterized Complexity. We resolve this open question by proposing an algorithm which solves this problem in O(15 k ∗ k ∗ m 3) and thus we show
Efficient Algorithms Using The Multiplicative Weights Update Method
, 2006
"... Abstract Algorithms based on convex optimization, especially linear and semidefinite programming, are ubiquitous in Computer Science. While there are polynomial time algorithms known to solve such problems, quite often the running time of these algorithms is very high. Designing simpler and more eff ..."
Abstract

Cited by 28 (1 self)
 Add to MetaCart
, and constraint satisfaction problems such as Min UnCut and Min 2CNF Deletion. 2. An ~O(n3) time derandomization of the AlonRoichman construction of expanders using Cayley graphs. The algorithm yields a set of O(log n) elements which generates an expanding Cayley graph in any group of n elements. 3. An ~O(n3
Accelerated Deletionbased Extraction of Minimal Unsatisfiable Cores
, 2014
"... Various technologies are based on the capability to find small unsatisfiable cores given an unsatisfiable CNF formula, i.e., a subset of the clauses that are unsatisfiable regardless of the rest of the formula. If that subset is irreducible, it is called a Minimal Unsatisfiable Core (MUC). In many c ..."
Abstract
 Add to MetaCart
Various technologies are based on the capability to find small unsatisfiable cores given an unsatisfiable CNF formula, i.e., a subset of the clauses that are unsatisfiable regardless of the rest of the formula. If that subset is irreducible, it is called a Minimal Unsatisfiable Core (MUC). In many
Satisfiability Allows No Nontrivial Sparsification Unless The PolynomialTime Hierarchy Collapses
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 38 (2010)
, 2010
"... Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small ..."
Abstract

Cited by 56 (2 self)
 Add to MetaCart
d ≥ 2. The case d = 2 implies that no NPhard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k 2−ǫ) edges unless coNP is in NP/poly, where k denotes the size of the deletion set. Kernels consisting of O(k 2) edges are known
On Subclasses of Minimal Unsatisfiable Formulas
 Discrete Applied Mathematics
"... We consider the minimal unsatisfiablity problem MU (k) for propositional formulas in conjunctive normal form (CNF) over n variables and n + k clauses, where k is fixed. It will be shown that MU (k) is in NP. Based on the nondeterministic algorithm we prove for MU(2) that after a simplification by ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
We consider the minimal unsatisfiablity problem MU (k) for propositional formulas in conjunctive normal form (CNF) over n variables and n + k clauses, where k is fixed. It will be shown that MU (k) is in NP. Based on the nondeterministic algorithm we prove for MU(2) that after a simplification
Tradeoffs in the complexity of backdoor detection
 In Principles and Practice of Constraint Programming  CP 2007
, 2007
"... Abstract. There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are “easily ” identifiable, while others are of interest because they capture key aspects of stateoft ..."
Abstract

Cited by 23 (5 self)
 Add to MetaCart
oftheart constraint solvers. In particular, it was recently shown that the problem of identifying a strong Horn or 2CNFbackdoor can be solved by exploiting equivalence with deletion backdoors, and is NPcomplete. We prove that strong backdoor identification becomes harder than NP (unless NP=coNP) as soon
Simplification: tableaux response to DP and KSAT methods
, 1997
"... f, and before applying any other rule, a simplification rule deletes all its other occurrences (at any level of nesting) and perform some suitable boolean reduction. 2 Theoretical Results A number of techniques can be shown to be restricted forms of a local simplification rule (LSR): ffl The DPLL ..."
Abstract
 Add to MetaCart
f, and before applying any other rule, a simplification rule deletes all its other occurrences (at any level of nesting) and perform some suitable boolean reduction. 2 Theoretical Results A number of techniques can be shown to be restricted forms of a local simplification rule (LSR): ffl
Results 1  10
of
16