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Vorapong Suppakitpaisarn

Publications and source records attributed to Vorapong Suppakitpaisarn.

22 records · Page 2Linked to original sources
arXiv2022

Worst-Case Analysis of LPT Scheduling on Small Number of Non-Identical Processors

The approximation ratio of the longest processing time (LPT) scheduling algorithm has been studied in several papers. While the tight approximation ratio is known for the case when all processors are identical, the ratio is not yet known when the processors have different speeds. In this work, we give a tight approximation ratio for the case when the number of processors is 3,4, and 5. We show that the ratio for those cases are no more than the lower bound provided by Gonzalez, Ibarra, and Sahni (SIAM J. Computing 1977). They are approximately 1.38 for three processors, 1.43 for four processors, and 1.46 for five processors.

cs.DM↗
arXiv2020

On the Size of Minimal Separators for Treedepth Decomposition

Treedepth decomposition has several practical applications and can be used to speed up many parameterized algorithms. There are several works aiming to design a scalable algorithm to compute exact treedepth decompositions. Those include works based on a set of all minimal separators. In those algorithms, although a number of minimal separators are enumerated, the minimal separators that are used for an optimal solution are empirically very small. Therefore, analyzing the upper bound on the size of minimal separators is an important problem because it has the potential to significantly reduce the computation time. A minimal separator $S$ is called an optimal top separator if $td(G) = |S| + td(G \backslash S)$, where $td(G)$ denotes the treedepth of $G$. Then, we have two theoretical results on the size of optimal top separators. (1) For any $G$, there is an optimal top separator $S$ such that $|S| \le 2tw(G)$, where $tw(G)$ is the treewidth of $G$. (2) For any $c < 2$, there exists a graph $G$ such that any optimal top separator $S$ of $G$ have $|S| > c \cdot tw(G)$, i.e., the first result gives a tight bound on the size of an optimal top separator.

cs.DS↗
arXiv2019

On the minimal Hamming weight of a multi-base representation

Given a finite set of bases $b_1$, $b_2$, \dots, $b_r$ (integers greater than $1$), a multi-base representation of an integer~$n$ is a sum with summands $db_1^{α_1}b_2^{α_2} \cdots b_r^{α_r}$, where the $α_j$ are nonnegative integers and the digits $d$ are taken from a fixed finite set. We consider multi-base representations with at least two bases that are multiplicatively independent. Our main result states that the order of magnitude of the minimal Hamming weight of an integer~$n$, i.e., the minimal number of nonzero summands in a representation of~$n$, is $\log n / (\log \log n)$. This is independent of the number of bases, the bases themselves, and the digit set. For the proof, the existing upper bound for prime bases is generalized to multiplicatively independent bases, for the required analysis of the natural greedy algorithm, an auxiliary result in Diophantine approximation is derived. The lower bound follows by a counting argument and alternatively by using communication complexity, thereby improving the existing bounds and closing the gap in the order of magnitude. This implies also that the greedy algorithm terminates after $\mathcal{O}(\log n/\log \log n)$ steps, and that this bound is sharp.

math.NT↗