H. Bodlaender and D. Kratsch, private communication, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Turing way for W[2] consider the following problem: Steiner Tree Instance: A graph G = V; E) a set S V ; a positive integer k. Parameter: k. Question: Is there a set of vertices T V S such that jT j k and G[S[T ] is connected This parameterized version of Steiner Tree is W[2] hard [3]. Notice however that the parameterized version in which k is unbounded and jSj is a parameter is xed parameter tractable [12] Although no membership result for this problem was previously known, we can easily place it in W[2] by devising a multi tape Turing machine that guesses a subset of ....

....problem: Balanced Separator Instance: A graph G = V; E) a positive integer k. Parameter: k. Question: Does there exist a subset S of at most k vertices such that each connected component of G [V S] has at most jV j vertices This parameterized problem is W[1] hard (reduction from Clique [3]) as far as we know, no membership result was previously known. Theorem 7 The Balanced Separator problem belongs to W[P] Proof. We show a parameterized reduction from Balanced Separator to the Bounded Nondeterminism Turing Machine Computation problem. Since the latter problem is ....

H. L. Bodlaender, D. Kratsch. Private communication, 1994.

.... vertices S V of cardinality at most k such that every connected component of G[V S] has at most jV j vertices ( 2 (0; 1) is a xed constant) Parameter: k W[1] hard, in W[P] membership: reduction to Bounded Nondeterminism Turing Machine Computation [38] hardness: reduction from Clique [24]) 2 Bandwidth Instance: A graph G = V; E) a positive integer k. Question: Is there a 1:1 linear layout f : V f1; jV jg such that (u; v) 2 E implies jf(u) f(v)j k Parameter: k W[t] hard for all t (reduction from Uniform Emulation On A Path [17] the problem remains W[t] hard ....

....r Subsets. Dominating Clique Instance: A graph G = V; E) a positive integer k. Question: Is there a set of k vertices V 0 V that forms a complete subgraph of G and is also a dominating set of G Parameter: k W[2] complete (membership is trivial; hardness: reduction from Dominating Set [24]; the problem is in FPT if V 0 is also required to be ecient, that is, each vertex not in V 0 is dominated by exactly one vertex in V 0 [24] Dominating Set Instance: A graph G = V; E) a positive integer k. Question: Is there a set of k vertices V 0 V with the property that every ....

[Article contains additional citation context not shown here]

H. L. Bodlaender and D. Kratsch, 1994. Private communication.

....occurs. It is not hard to define a PSPACE hard function that does have a PTAS, but the straightforward examples are artificial. We were thus led to ask in [8, 9] whether there is a natural PSPACE hard function that has a PTAS. A positive answer to this question is provided in [19] Bodlaender [5] has extended our results by showing that MAX Q 3SAT can be approximated within some 0 ffl 1 and by providing a simpler proof of the fact that MAX GGEOG is PSPACE hard to approximate; his proof that approximating MAX GGEOG is hard does not involve PCDS s. Hunt et al. 14] showed, also using ....

H. Bodlaender. Private communication.

No context found.

H. Bodlaender and D. Kratsch, private communication, 1994.

No context found.

H. L. Bodlaender, private communication, 1994. 26

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC