On the Combinatorial Complexity of Motion Coordination
On the Combinatorial Complexity of Motion Coordination
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Can we move them in the plane so that their final positions cover a given set of m points? Remarks : Remains NP-hard even if r is constant and no osbstacles exist. Reduction from 3-SATISFIABILITY Note : References for the NP-coraplete problems which furnish a basis for our arguments, can be found in [GJ, 79]. 3. NP-hardness results for planning pebble motion on a graph ONE PASS PEBBLE MOTION IN PLANAR GRAPHS (P6) Given a planar graph G = (V, E) with ail vertices in V being one-pass. Given also ...a collection I = {s, ,. .. , s. } E V, s = {tp. .. , t^} E V and ^i. '^j such that j * i L^ * l^, s^ i^ Sj, s^ # ty A pebble named p. Is originally placed on each s^, i ~ 1, . ^ . , k. Is there a way of moving each p. From initial pcr. Ltlon's, to frlnrl position t. By a sequence of legal moves? Re ma r k Transf pncation from "k-vertex DISJOINT PATHS IN PLANAR GRAPHS", k is p^. T of the input. PEBBLE MOTION WITH NON-ADJACENCY (P7) Let there be given a planar graph G = (V, E) such that maximum degree of each vertex u e V is
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To quickly assess the difficulty of the text, read a short excerpt:
Can we move them in the plane so that their final positions cover a given set of m points? Remarks : Remains NP-hard even if r is constant and no osbstacles exist. Reduction from 3-SATISFIABILITY Note : References for the NP-coraplete problems which furnish a basis for our arguments, can be found in [GJ, 79]. 3. NP-hardness results for planning pebble motion on a graph ONE PASS PEBBLE MOTION IN PLANAR GRAPHS (P6) Given a planar graph G = (V, E) with ail vertices in V being one-pass. Given also ...a collection I = {s, ,. .. , s. } E V, s = {tp. .. , t^} E V and ^i. '^j such that j * i L^ * l^, s^ i^ Sj, s^ # ty A pebble named p. Is originally placed on each s^, i ~ 1, . ^ . , k. Is there a way of moving each p. From initial pcr. Ltlon's, to frlnrl position t. By a sequence of legal moves? Re ma r k Transf pncation from "k-vertex DISJOINT PATHS IN PLANAR GRAPHS", k is p^. T of the input. PEBBLE MOTION WITH NON-ADJACENCY (P7) Let there be given a planar graph G = (V, E) such that maximum degree of each vertex u e V is
What to read after On the Combinatorial Complexity of Motion Coordination?
You can find similar books in the "Read Also" column, or choose other free books by Paul G Spirakis to read onlineMoreLess
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