arXiv subjects

Sungjin Im

Publications and source records attributed to Sungjin Im.

41 records · Page 3Linked to original sources

arXiv2013

Optimizing Maximum Flow Time and Maximum Throughput in Broadcast Scheduling

We consider the pull-based broadcast scheduling model. In this model, there are n unit-sized pages of information available at the server. Requests arrive over time at the server asking for a specific page. When the server transmits a page, all outstanding requests for the page are simultaneously satisfied, and this is what distinguishes broadcast scheduling from the standard scheduling setting where each job must be processed separately by the server. Broadcast scheduling has received a considerable amount of attention due to the algorithmic challenges that it gives in addition to its applications in multicast systems and wireless and LAN networks. In this paper, we give the following new approximation results for two popular objectives: - For the objective of minimizing the maximum flow time, we give the first PTAS. Previously, it was known that the algorithm First-In-First-Out (FIFO) is a 2-approximation, and it is tight. It has been suggested as an open problem to obtain a better approximation. - For the objective of maximizing the throughput, we give a 0.7759-approximation which improves upon the previous best known 0.75-approximation. Our improved results are enabled by our novel rounding schemes and linear programming which can effectively reduce congestion in schedule which is often the main bottleneck in designing scheduling algorithms based on linear programming. We believe that our algorithmic ideas and techniques could be of potential use for other scheduling problems.

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arXiv2013

Minimum Latency Submodular Cover

We study the Minimum Latency Submodular Cover problem (MLSC), which consists of a metric $(V,d)$ with source $r\in V$ and $m$ monotone submodular functions $f_1, f_2, ..., f_m: 2^V \rightarrow [0,1]$. The goal is to find a path originating at $r$ that minimizes the total cover time of all functions. This generalizes well-studied problems, such as Submodular Ranking [AzarG11] and Group Steiner Tree [GKR00]. We give a polynomial time $O(\log \frac{1}{\eps} \cdot \log^{2+δ} |V|)$-approximation algorithm for MLSC, where $ε>0$ is the smallest non-zero marginal increase of any $\{f_i\}_{i=1}^m$ and $δ>0$ is any constant. We also consider the Latency Covering Steiner Tree problem (LCST), which is the special case of \mlsc where the $f_i$s are multi-coverage functions. This is a common generalization of the Latency Group Steiner Tree [GuptaNR10a,ChakrabartyS11] and Generalized Min-sum Set Cover [AzarGY09, BansalGK10] problems. We obtain an $O(\log^2|V|)$-approximation algorithm for LCST. Finally we study a natural stochastic extension of the Submodular Ranking problem, and obtain an adaptive algorithm with an $O(\log 1/ \eps)$ approximation ratio, which is best possible. This result also generalizes some previously studied stochastic optimization problems, such as Stochastic Set Cover [GoemansV06] and Shared Filter Evaluation [MunagalaSW07, LiuPRY08].

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arXiv2011

Fast Clustering using MapReduce

Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming environment for processing large datasets. We focus on the practical and popular clustering problems, $k$-center and $k$-median. We develop fast clustering algorithms with constant factor approximation guarantees. From a theoretical perspective, we give the first analysis that shows several clustering algorithms are in $\mathcal{MRC}^0$, a theoretical MapReduce class introduced by Karloff et al. \cite{KarloffSV10}. Our algorithms use sampling to decrease the data size and they run a time consuming clustering algorithm such as local search or Lloyd's algorithm on the resulting data set. Our algorithms have sufficient flexibility to be used in practice since they run in a constant number of MapReduce rounds. We complement these results by performing experiments using our algorithms. We compare the empirical performance of our algorithms to several sequential and parallel algorithms for the $k$-median problem. The experiments show that our algorithms' solutions are similar to or better than the other algorithms' solutions. Furthermore, on data sets that are sufficiently large, our algorithms are faster than the other parallel algorithms that we tested.

cs.DC↗

arXiv2009

Longest Wait First for Broadcast Scheduling

We consider online algorithms for broadcast scheduling. In the pull-based broadcast model there are $n$ unit-sized pages of information at a server and requests arrive online for pages. When the server transmits a page $p$, all outstanding requests for that page are satisfied. The longest-wait-first} (LWF) algorithm is a natural algorithm that has been shown to have good empirical performance. In this paper we make two main contributions to the analysis of LWF and broadcast scheduling. \begin{itemize} \item We give an intuitive and easy to understand analysis of LWF which shows that it is $O(1/\eps^2)$-competitive for average flow-time with $(4+\eps)$ speed. Using a more involved analysis, we show that LWF is $O(1/\eps^3)$-competitive for average flow-time with $(3.4+ε)$ speed. \item We show that a natural extension of LWF is O(1)-speed O(1)-competitive for more general objective functions such as average delay-factor and $L_k$ norms of delay-factor (for fixed $k$). \end{itemize}

cs.DS↗

arXiv2009

Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling

We consider online algorithms for pull-based broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, namely maximum response time (waiting time) and maximum delay-factor and their weighted versions. We obtain the following results in the worst-case online competitive model. - We show that FIFO (first-in first-out) is 2-competitive even when the page sizes are different. Previously this was known only for unit-sized pages [10] via a delicate argument. Our proof differs from [10] and is perhaps more intuitive. - We give an online algorithm for maximum delay-factor that is O(1/eps^2)-competitive with (1+\eps)-speed for unit-sized pages and with (2+\eps)-speed for different sized pages. This improves on the algorithm in [12] which required (2+\eps)-speed and (4+\eps)-speed respectively. In addition we show that the algorithm and analysis can be extended to obtain the same results for maximum weighted response time and delay factor. - We show that a natural greedy algorithm modeled after LWF (Longest-Wait-First) is not O(1)-competitive for maximum delay factor with any constant speed even in the setting of standard scheduling with unit-sized jobs. This complements our upper bound and demonstrates the importance of the tradeoff made in our algorithm.

cs.DS↗