Yuval Filmus

Master's thesis

We consider the NP-complete optimization problem *Bandwidth*. Anupam Gupta gave an $O(\log^{2.5} n)$ approximation algorithm for trees, and showed that his algorithm has an approximation ratio of $O(\log n)$ on *caterpillars*, trees composed of a central path and paths emanating from it. We show that the same approximation ratio is obtained on trees composed of a central path and caterpillars emanating from it.

Our result relies on the following lemma.

**Definition.** A sequence $a_1,\ldots,a_n$ has *thickness* $\Theta$ if the sum of any $d$ consecutive elements is at most $d\Theta$, for $1 \leq d \leq n$.

**Lemma.** If a sequence has thickness $\Theta$, then the sequence obtained by ordering the elements in non-decreasing order also has thickness $\Theta$.

@mastersthesis{Filmus2002,

author = {Yuval Filmus},

title = {Bandwidth approximation of a restricted family of trees},

school = {Weizmann institute of science},

year = {2002}

}

copy to clipboard
author = {Yuval Filmus},

title = {Bandwidth approximation of a restricted family of trees},

school = {Weizmann institute of science},

year = {2002}

}