Extracting pure network submatrices in linear programs using signed graphs
Discrete Applied Mathematics
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized algorithms for feedback set problems and their duals in tournaments
Theoretical Computer Science - Parameterized and exact computation
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
Optimal edge deletions for signed graph balancing
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Note on maximal bisection above tight lower bound
Information Processing Letters
Fast and Efficient Bright-Field AAPSM Conflict Detection and Correction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Max-cut parameterized above the edwards-erdős bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Parameterized Complexity
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We consider graphs without loops or parallel edges in which every edge is assigned + or -. Such a signed graph is balanced if its vertex set can be partitioned into parts V"1 and V"2 such that all edges between vertices in the same part have sign + and all edges between vertices of different parts have sign - (one of the parts may be empty). It is well-known that every connected signed graph with n vertices and m edges has a balanced subgraph with at least m2+n-14 edges and this bound is tight. We consider the following parameterized problem: given a connected signed graph G with n vertices and m edges, decide whether G has a balanced subgraph with at least m2+n-14+k4 edges, where k is the parameter. We obtain an algorithm for the problem of runtime 8^k(kn)^O^(^1^). We also prove that for each instance (G,k) of the problem, in polynomial time, we can either solve (G,k) or produce an equivalent instance (G^',k^') such that k^'=