Search Results

Documents authored by Wolf, Joel

Found 2 Possible Name Variants:

Wolf, Joel L.

Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.416
The Container Selection Problem

Authors: Viswanath Nagarajan, Kanthi K. Sarpatwar, Baruch Schieber, Hadas Shachnai, and Joel L. Wolf

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
We introduce and study a network resource management problem that is a special case of non-metric k-median, naturally arising in cross platform scheduling and cloud computing. In the continuous d-dimensional container selection problem, we are given a set C of input points in d-dimensional Euclidean space, for some d >= 2, and a budget k. An input point p can be assigned to a "container point" c only if c dominates p in every dimension. The assignment cost is then equal to the L1-norm of the container point. The goal is to find k container points in the d-dimensional space, such that the total assignment cost for all input points is minimized. The discrete variant of the problem has one key distinction, namely, the container points must be chosen from a given set F of points. For the continuous version, we obtain a polynomial time approximation scheme for any fixed dimension d>= 2. On the negative side, we show that the problem is NP-hard for any d>=3. We further show that the discrete version is significantly harder, as it is NP-hard to approximate without violating the budget k in any dimension d>=3. Thus, we focus on obtaining bi-approximation algorithms. For d=2, the bi-approximation guarantee is (1+epsilon,3), i.e., for any epsilon>0, our scheme outputs a solution of size 3k and cost at most (1+epsilon) times the optimum. For fixed d>2, we present a (1+epsilon,O((1/epsilon)log k)) bi-approximation algorithm.
Cite as

Viswanath Nagarajan, Kanthi K. Sarpatwar, Baruch Schieber, Hadas Shachnai, and Joel L. Wolf. The Container Selection Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 416-434, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{nagarajan_et_al:LIPIcs.APPROX-RANDOM.2015.416,
  author =	{Nagarajan, Viswanath and Sarpatwar, Kanthi K. and Schieber, Baruch and Shachnai, Hadas and Wolf, Joel L.},
  title =	{{The Container Selection Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{416--434},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.416},
  URN =		{urn:nbn:de:0030-drops-53153},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.416},
  annote =	{Keywords: non-metric k-median, geometric hitting set, approximation algorithms, cloud computing, cross platform scheduling.}
}

Wolf, Joel

Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.185
Scheduling with Setup Costs and Monotone Penalties

Authors: Rohit Khandekar, Kirsten Hildrum, Deepak Rajan, and Joel Wolf

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
We consider single processor preemptive scheduling with job-dependent setup times. In this model, a job-dependent setup time is incurred when a job is started for the first time, and each time it is restarted after preemption. This model is a common generalization of preemptive scheduling, and actually of non-preemptive scheduling as well. The objective is to minimize the sum of any general non-negative, non-decreasing cost functions of the completion times of the jobs -- this generalizes objectives of minimizing weighted flow time, flow-time squared, tardiness or the number of tardy jobs among many others. Our main result is a randomized polynomial time O(1)-speed O(1)-approximation algorithm for this problem. Without speedup, no polynomial time finite multiplicative approximation is possible unless P=NP. We extend the approach of Bansal et al. (FOCS 2007) of rounding a linear programming relaxation which accounts for costs incurred due to the non-preemptive nature of the schedule. A key new idea used in the rounding is that a point in the intersection polytope of two matroids can be decomposed as a convex combination of incidence vectors of sets that are independent in both matroids. In fact, we use this for the intersection of a partition matroid and a laminar matroid, in which case the decomposition can be found efficiently using network flows. Our approach gives a randomized polynomial time offline O(1)-speed O(1)-approximation algorithm for the broadcast scheduling problem with general cost functions as well.
Cite as

Rohit Khandekar, Kirsten Hildrum, Deepak Rajan, and Joel Wolf. Scheduling with Setup Costs and Monotone Penalties. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 185-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

Copy BibTex To Clipboard

@InProceedings{khandekar_et_al:LIPIcs.FSTTCS.2012.185,
  author =	{Khandekar, Rohit and Hildrum, Kirsten and Rajan, Deepak and Wolf, Joel},
  title =	{{Scheduling with Setup Costs and Monotone Penalties}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{185--198},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.185},
  URN =		{urn:nbn:de:0030-drops-38576},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.185},
  annote =	{Keywords: Scheduling, resource augmentation, approximation algorithm, preemption, setup times}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2009.2325
Bounded Size Graph Clustering with Applications to Stream Processing

Authors: Rohit Khandekar, Kirsten Hildrum, Sujay Parekh, Deepak Rajan, Jay Sethuraman, and Joel Wolf

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
We introduce a graph clustering problem motivated by a stream processing application. Input to our problem is an undirected graph with vertex and edge weights. A cluster is a subset of the vertices. The {\em size} of a cluster is defined as the total vertex weight in the subset plus the total edge weight at the boundary of the cluster. The bounded size graph clustering problem ($\GC$) is to partition the vertices into clusters of size at most a given budget and minimize the total edge-weight across the clusters. In the {\em multiway cut} version of the problem, we are also given a subset of vertices called {\em terminals}. No cluster is allowed to contain more than one terminal. Our problem differs from most of the previously studied clustering problems in that the number of clusters is not specified. We first show that the feasibility version of the multiway cut $\GC$ problem, i.e., determining if there exists a clustering with bounded-size clusters satisfying the multiway cut constraint, can be solved in polynomial time. Our algorithm is based on the min-cut subroutine and an uncrossing argument. This result is in contrast with the NP-hardness of the min-max multiway cut problem, considered by Svitkina and Tardos (2004), in which the number of clusters must equal the number of terminals. Our results for the feasibility version also generalize to any symmetric submodular function. We next show that the optimization version of $\GC$ is NP-hard by showing an approximation-preserving reduction from the $\frac 13$-balanced cut problem. Our main result is an $O(\log^2 n)$-approximation to the optimization version of the multiway cut $\GC$ problem violating the budget by an $O(\log n)$ factor, where $n$ denotes the number of vertices. Our algorithm is based on a set-cover-like greedy approach which iteratively computes bounded-size clusters to maximize the number of new vertices covered.
Cite as

Rohit Khandekar, Kirsten Hildrum, Sujay Parekh, Deepak Rajan, Jay Sethuraman, and Joel Wolf. Bounded Size Graph Clustering with Applications to Stream Processing. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{khandekar_et_al:LIPIcs.FSTTCS.2009.2325,
  author =	{Khandekar, Rohit and Hildrum, Kirsten and Parekh, Sujay and Rajan, Deepak and Sethuraman, Jay and Wolf, Joel},
  title =	{{Bounded Size Graph Clustering with Applications to Stream Processing}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{275--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2325},
  URN =		{urn:nbn:de:0030-drops-23250},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2325},
  annote =	{Keywords: Graph partitioning, uncrossing, Gomory-Hu trees, symmetric submodular functions}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact