Name
Abstract | ||
|---|---|---|
We consider the worst-case query complexity of some variants of certain P P A D complete search problems. Suppose we are given a graph G and a vertex s is an element of V (G). We denote the directed graph obtained from G by directing all edges in both directions by G'. D is a directed subgraph of G' which is unknown to us, except that it consists of vertex-disjoint directed paths and cycles and one of the paths originates in s. Our goal is to find an endvertex of a path by using as few queries as possible. A query specifies a vertex v is an element of V (G), and the answer is the set of the edges of D incident to v, together with their directions. We also show lower bounds for the special case when D consists of a single path. Our proofs use the theory of graph separators. Finally, we consider the case when the graph G is a grid graph. In this case, using the connection with separators, we give asymptotically tight bounds as a function of the size of the grid, if the dimension of the grid is considered as fixed. In order to do this, we prove a separator theorem about grid graphs, which is interesting on its own right. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.26493/1855-3974.788.89a | ARS MATHEMATICA CONTEMPORANEA |
Keywords | Field | DocType |
Separator,graph,search,grid | Graph,Combinatorics,Vertex (geometry),Directed graph,Mathematical proof,Lattice graph,Grid,Mathematics,PPAD,Special case | Journal |
Volume | Issue | ISSN |
12 | 2 | 1855-3966 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dániel Gerbner | 1 | 46 | 21.61 |
| Balázs Keszegh | 2 | 156 | 24.36 |
| Dömötör Pálvölgyi | 3 | 202 | 29.14 |
| Günter Rote | 4 | 1181 | 129.29 |
| Gábor Wiener | 5 | 64 | 10.65 |