Abstract
We give an algorithmic and lower bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding algorithms with running time 2(O(n1-1/d)) for any fixed dimension d >= 2 for many well-known graph problems, including INDEPENDENT SET, r-DOMINATING SET for constant r, and STEINER TREE. For most problems, we get improved running times compared to prior work; in some cases, we give the first known subexponential algorithm in geometric intersection graphs. Additionally, most of the obtained algorithms are representation-agnostic, i.e., they work on the graph itself and do not require the geometric representation. Our algorithmic framework is based on a weighted separator theorem and various treewidth techniques. The lower bound framework is based on a constructive embedding of graphs into d-dimensional grids, and it allows us to derive matching 2(Omega(n1-1/d)) lower bounds under the exponential time hypothesis even in the much more restricted class of d-dimensional induced grid graphs.
Original language | English |
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Pages (from-to) | 1291-1331 |
Number of pages | 41 |
Journal | Siam Journal on Computing |
Volume | 49 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- unit disk graph
- separator
- fat objects
- subexponential
- ETH
- COMPLEXITY
- TREEWIDTH
- PATHS
- SET