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Documents authored by Edmonds, Jeff


Document
Hardness of Function Composition for Semantic Read once Branching Programs

Authors: Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)


Abstract
In this work, we study time/space trade-offs for function composition. We prove asymptotically optimal lower bounds for function composition in the setting of nondeterministic read once branching programs, for the syntactic model as well as the stronger semantic model of read-once nondeterministic computation. We prove that such branching programs for solving the tree evaluation problem over an alphabet of size k requires size roughly k^{Omega(h)}, i.e space Omega(h log k). Our lower bound nearly matches the natural upper bound which follows the best strategy for black-white pebbling the underlying tree. While previous super-polynomial lower bounds have been proven for read-once nondeterministic branching programs (for both the syntactic as well as the semantic models), we give the first lower bounds for iterated function composition, and in these models our lower bounds are near optimal.

Cite as

Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi. Hardness of Function Composition for Semantic Read once Branching Programs. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 15:1-15:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{edmonds_et_al:LIPIcs.CCC.2018.15,
  author =	{Edmonds, Jeff and Medabalimi, Venkatesh and Pitassi, Toniann},
  title =	{{Hardness of Function Composition for Semantic Read once Branching Programs}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.15},
  URN =		{urn:nbn:de:0030-drops-88747},
  doi =		{10.4230/LIPIcs.CCC.2018.15},
  annote =	{Keywords: Branching Programs, Function Composition, Time-Space Tradeoffs, Semantic Read Once, Tree Evaluation Problem}
}
Document
Lower Bounds for Nondeterministic Semantic Read-Once Branching Programs

Authors: Stephen Cook, Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)


Abstract
We prove exponential lower bounds on the size of semantic read-once 3-ary nondeterministic branching programs. Prior to our result the best that was known was for D-ary branching programs with |D| >= 2^{13}.

Cite as

Stephen Cook, Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi. Lower Bounds for Nondeterministic Semantic Read-Once Branching Programs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 36:1-36:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{cook_et_al:LIPIcs.ICALP.2016.36,
  author =	{Cook, Stephen and Edmonds, Jeff and Medabalimi, Venkatesh and Pitassi, Toniann},
  title =	{{Lower Bounds for Nondeterministic Semantic Read-Once Branching Programs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.36},
  URN =		{urn:nbn:de:0030-drops-63166},
  doi =		{10.4230/LIPIcs.ICALP.2016.36},
  annote =	{Keywords: Branching Programs, Semantic, Non-deterministic, Lower Bounds}
}
Document
10071 Open Problems – Scheduling

Authors: Jim Anderson, Björn Andersson, Yossi Azar, Nikhil Bansal, Enrico Bini, Marek Chrobak, José Correa, Liliana Cucu-Grosjean, Rob Davis, Arvind Easwaran, Jeff Edmonds, Shelby Funk, Sathish Gopalakrishnan, Han Hoogeveen, Claire Mathieu, Nicole Megow, Seffi Naor, Kirk Pruhs, Maurice Queyranne, Adi Rosén, Nicolas Schabanel, Jiří Sgall, René Sitters, Sebastian Stiller, Marc Uetz, Tjark Vredeveld, and Gerhard J. Woeginger

Published in: Dagstuhl Seminar Proceedings, Volume 10071, Scheduling (2010)


Abstract
Collection of the open problems presented at the scheduling seminar.

Cite as

Jim Anderson, Björn Andersson, Yossi Azar, Nikhil Bansal, Enrico Bini, Marek Chrobak, José Correa, Liliana Cucu-Grosjean, Rob Davis, Arvind Easwaran, Jeff Edmonds, Shelby Funk, Sathish Gopalakrishnan, Han Hoogeveen, Claire Mathieu, Nicole Megow, Seffi Naor, Kirk Pruhs, Maurice Queyranne, Adi Rosén, Nicolas Schabanel, Jiří Sgall, René Sitters, Sebastian Stiller, Marc Uetz, Tjark Vredeveld, and Gerhard J. Woeginger. 10071 Open Problems – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{anderson_et_al:DagSemProc.10071.3,
  author =	{Anderson, Jim and Andersson, Bj\"{o}rn and Azar, Yossi and Bansal, Nikhil and Bini, Enrico and Chrobak, Marek and Correa, Jos\'{e} and Cucu-Grosjean, Liliana and Davis, Rob and Easwaran, Arvind and Edmonds, Jeff and Funk, Shelby and Gopalakrishnan, Sathish and Hoogeveen, Han and Mathieu, Claire and Megow, Nicole and Naor, Seffi and Pruhs, Kirk and Queyranne, Maurice and Ros\'{e}n, Adi and Schabanel, Nicolas and Sgall, Ji\v{r}{\'\i} and Sitters, Ren\'{e} and Stiller, Sebastian and Uetz, Marc and Vredeveld, Tjark and Woeginger, Gerhard J.},
  title =	{{10071 Open Problems – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10071},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.3},
  URN =		{urn:nbn:de:0030-drops-25367},
  doi =		{10.4230/DagSemProc.10071.3},
  annote =	{Keywords: Open problems, scheduling}
}
Document
Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold

Authors: Jeff Edmonds

Published in: Dagstuhl Seminar Proceedings, Volume 10071, Scheduling (2010)


Abstract
The goal is to prove a surprising lower bound for resource augmented nonclairvoyant algorithms for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time. Edmonds and Pruhs in SODA09 prove that for every $\e > 0$, there is an algorithm $\alg_{\e}$ that is $(1\!+\!\epsilon)$-speed $O({1 \over \e2})$-competitive. A problem, however, is that this algorithm $\alg_{\e}$ depends on $\e$. The goal is to prove that every fixed deterministic nonclairvoyant algorithm has a suboptimal speed threshold, namely for every (graceful) algorithm $\alg$, there is a threshold $1\!+\!\beta_{\alg}$ that is $\beta_{\alg} > 0$ away from being optimal such that the algorithm is $\Omega({1 \over \e \beta_{\alg}})$ competitive with speed $(1 \!+\! \beta_{\alg}) \!+\! \e$ and is $\omega(1)$ competitive with speed $1 \!+\! \beta_{\alg}$. I have worked very hard on it and have felt that I was close. The proof technique is to use Brouwer's fixed point theorem to break the cycle of needing to know which input will be given before one can know what the algorithm will do and needing to know what the algorithm will do before one can know which input to give. Every thing I have can be found at

Cite as

Jeff Edmonds. Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{edmonds:DagSemProc.10071.6,
  author =	{Edmonds, Jeff},
  title =	{{Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold}},
  booktitle =	{Scheduling},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10071},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.6},
  URN =		{urn:nbn:de:0030-drops-25447},
  doi =		{10.4230/DagSemProc.10071.6},
  annote =	{Keywords: Scheduling}
}
Document
Scalably Scheduling Processes with Arbitrary Speedup Curves

Authors: Jeff Edmonds and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 10071, Scheduling (2010)


Abstract
We give a scalable ((1+\epsilon)-speed O(1)-competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time.

Cite as

Jeff Edmonds and Kirk Pruhs. Scalably Scheduling Processes with Arbitrary Speedup Curves. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{edmonds_et_al:DagSemProc.10071.12,
  author =	{Edmonds, Jeff and Pruhs, Kirk},
  title =	{{Scalably Scheduling Processes with Arbitrary Speedup Curves}},
  booktitle =	{Scheduling},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10071},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.12},
  URN =		{urn:nbn:de:0030-drops-25463},
  doi =		{10.4230/DagSemProc.10071.12},
  annote =	{Keywords: Scheduling}
}
Document
Nonclairvoyant Speed Scaling for Flow and Energy

Authors: Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)


Abstract
We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is $P(s)=s^\alpha$. We give a nonclairvoyant algorithm that is shown to be $O(\alpha^3)$-competitive. We then show an $\Omega( \alpha^{1/3-\epsilon} )$ lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be $O(1)$-competitive.

Cite as

Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs. Nonclairvoyant Speed Scaling for Flow and Energy. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 255-264, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)


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@InProceedings{chan_et_al:LIPIcs.STACS.2009.1815,
  author =	{Chan, Ho-Leung and Edmonds, Jeff and Lam, Tak-Wah and Lee, Lap-Kei and Marchetti-Spaccamela, Alberto and Pruhs, Kirk},
  title =	{{Nonclairvoyant Speed Scaling for Flow and Energy}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{255--264},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1815},
  URN =		{urn:nbn:de:0030-drops-18151},
  doi =		{10.4230/LIPIcs.STACS.2009.1815},
  annote =	{Keywords: }
}
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