Parameterized and Exact Computation: 9th International by Marek Cygan, Pinar Heggernes

By Marek Cygan, Pinar Heggernes

This e-book constitutes the completely refereed post-conference complaints of the ninth overseas Symposium on Parameterized and targeted Computation, IPEC 2014, in Wroclaw, Poland, in September 2014. The 27 revised complete papers awarded including one invited paper have been rigorously reviewed and chosen from forty two submissions. the subjects addressed disguise learn in all points of parameterized/exact algorithms and complexity together with yet are usually not constrained to new concepts for the layout and research of parameterized and specified algorithms, fixed-parameter tractability effects; parameterized complexity thought, courting among parameterized complexity and conventional complexity classifications; purposes of parameterized and designated exponential-time computation; and implementation problems with parameterized and specified exponential-time algorithms.

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Additional resources for Parameterized and Exact Computation: 9th International Symposium, IPEC 2014, Wroclaw, Poland, September 10-12, 2014. Revised Selected Papers

Example text

We include the new equation i=1 j=1 Aij xj = n i=1 bi (obtained by adding up all equations in Ax = b) to obtain a new system A x = b . Note that Ax = b and A x = b have identical solutions. Furthermore, n n n the new equation i=1 j=1 Aij xj = i=1 bi has on its left-hand side precisely the sum of all single occurrence variables of the system Ax = b. Hence every variable in A x = b occurs exactly twice. 5 to design the algorithms in this subsection. 1. LinEq≤,k≤2 ∈ P. Proof. Given an instance (A, b, t) of LinEq≤,k≤2 , we construct the graph G associated with Ax = b.

Rq }, l) be any given instance of LCS. For each i = 1, . . , q, create a term ui as follows: ui = f (yi,1 , f (x1 , f (yi,2 , f (x2 , · · · f (yi,l , f (xl , f (yi,l+1 , g(#, #))) · · · )))), where # is a character not appearing in r1 , . . , rq . Create a term t1 by replacing the last occurrence of # in each ui by ui+1 for i = 1, . . , q − 1, thus concatenating u1 , . . , uq , as shown in Fig. 1. , & does not match any symbol but can match any variable). Represent each ri by a term ti defined by: ti = f (ri [1], f (ri [2], f (ri [3], f (· · · , f (ri [1 + 2 · |ri |], g(#, #)) · · · )))).

The next theorem, whose proof is omitted in this version, shows that associative-commutative matching is W [1]-hard even if every function is associative and commutative. Theorem 9. Matching is W [1]-hard with respect to the number of variables even if every function symbol is associative and commutative. On the other hand, associative-commutative matching can be done in polynomial time if t1 is a DO-term [5]. We can extend this algorithm to the special case of unification where both terms are DO-terms by adding a condition in the algorithm that f ((t1 )u1 , .

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