Bandwidth Approximation of a Restricted Family of Trees
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چکیده
Bandwidth is one of the canonical NP-complete problems [17]. It is NP-hard to approximate within any constant, even on trees [22]. Gupta gave a randomized approximation algorithm [8] for bandwidth on trees, which has an approximation ratio of O(log n). This algorithm has the best currently known approximation ratio on trees. Gupta showed that his algorithm has an approximation ratio of O(log n) on caterpillars, a restricted family of trees. We show that Gupta’s algorithm has an approximation ratio of O(log n) on manycaterpillars, an extension of caterpillars. We also simplify and derandomize Gupta’s algorithm on many-caterpillars.
منابع مشابه
Parameterized Complexity of Bandwidth on Trees
The bandwidth of a n-vertex graph G is the smallest integer b such that there exists a bijective function f : V (G) → {1, ..., n}, called a layout of G, such that for every edge uv ∈ E(G), |f(u)− f(v)| ≤ b. In the Bandwidth problem we are given as input a graph G and integer b, and asked whether the bandwidth of G is at most b. We present two results concerning the parameterized complexity of t...
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