# Search Results

### Documents authored by Jacob, Riko

Document
##### An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio

Authors: Mayank Goswami and Riko Jacob

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

##### Abstract
The problem of sorting with priced information was introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is to find a sorting algorithm with small competitive ratio, defined as the (worst-case) ratio of the algorithm’s cost to the cost of the cheapest proof of the sorted order. The simple case of bichromatic sorting posed by [CFGKRS] remains open: We are given two sets A and B of total size N, and the cost of an A-A comparison or a B-B comparison is higher than an A-B comparison. The goal is to sort A ∪ B. An Ω(log N) lower bound on competitive ratio follows from unit-cost sorting. Note that this is a generalization of the famous nuts and bolts problem, where A-A and B-B comparisons have infinite cost, and elements of A and B are guaranteed to alternate in the final sorted order. In this paper we give a randomized algorithm InversionSort with an almost-optimal w.h.p. competitive ratio of O(log³ N). This is the first algorithm for bichromatic sorting with a o(N) competitive ratio.

##### Cite as

Mayank Goswami and Riko Jacob. An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 56:1-56:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

```@InProceedings{goswami_et_al:LIPIcs.ITCS.2024.56,
author =	{Goswami, Mayank and Jacob, Riko},
title =	{{An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio}},
booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
pages =	{56:1--56:17},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-309-6},
ISSN =	{1868-8969},
year =	{2024},
volume =	{287},
editor =	{Guruswami, Venkatesan},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.56},
URN =		{urn:nbn:de:0030-drops-195843},
doi =		{10.4230/LIPIcs.ITCS.2024.56},
annote =	{Keywords: Sorting, Priced Information, Nuts and Bolts}
}```
Document
##### Fragile Complexity of Comparison-Based Algorithms

Authors: Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

##### Abstract
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes part in. We give a number of upper and lower bounds on the fragile complexity for fundamental problems, including Minimum, Selection, Sorting and Heap Construction. The results include both deterministic and randomized upper and lower bounds, and demonstrate a separation between the two settings for a number of problems. The depth of a comparator network is a straight-forward upper bound on the worst case fragile complexity of the corresponding fragile algorithm. We prove that fragile complexity is a different and strictly easier property than the depth of comparator networks, in the sense that for some problems a fragile complexity equal to the best network depth can be achieved with less total work and that with randomization, even a lower fragile complexity is possible.

##### Cite as

Peyman Afshani, Rolf Fagerberg, David Hammer, Riko Jacob, Irina Kostitsyna, Ulrich Meyer, Manuel Penschuck, and Nodari Sitchinava. Fragile Complexity of Comparison-Based Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

```@InProceedings{afshani_et_al:LIPIcs.ESA.2019.2,
author =	{Afshani, Peyman and Fagerberg, Rolf and Hammer, David and Jacob, Riko and Kostitsyna, Irina and Meyer, Ulrich and Penschuck, Manuel and Sitchinava, Nodari},
title =	{{Fragile Complexity of Comparison-Based Algorithms}},
booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
pages =	{2:1--2:19},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-124-5},
ISSN =	{1868-8969},
year =	{2019},
volume =	{144},
editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.2},
URN =		{urn:nbn:de:0030-drops-111235},
doi =		{10.4230/LIPIcs.ESA.2019.2},
annote =	{Keywords: Algorithms, comparison based algorithms, lower bounds}
}```
Document
##### External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms

Authors: John Iacono, Riko Jacob, and Konstantinos Tsakalidis

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

##### Abstract
We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in O(1/Blog_{M/B} N/B) amortized I/Os and operations ExtractMin and Delete in O(ceil[(M^epsilon)/B log_{M/B} N/B] log_{M/B} N/B) amortized I/Os, for any real epsilon in (0,1), using O(N/Blog_{M/B} N/B) blocks. Previous I/O-efficient priority queues either support these operations in O(1/Blog_2 N/B) amortized I/Os [Kumar and Schwabe, SPDP '96] or support only operations Insert, Delete and ExtractMin in optimal O(1/Blog_{M/B} N/B) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS '99]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O(1/Blog_M/B N/B) I/Os and operation Extract on K extracted elements in O(M^{epsilon} log_M/B N/B + K/B) amortized I/Os, using O(N/B) blocks. Previous results achieve O(1/Blog_2 N/B) I/Os and O(log_2 N/B + K/B) I/Os, respectively [Buchsbaum et al., SODA '00]. Our results imply improved O(E/Blog_{M/B} E/B) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E) with E = Omega (V^(1+epsilon)), epsilon > 0 and V = Omega (M), which is equal to the I/O-optimal bound for sorting E values in external memory.

##### Cite as

John Iacono, Riko Jacob, and Konstantinos Tsakalidis. External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

```@InProceedings{iacono_et_al:LIPIcs.ESA.2019.60,
author =	{Iacono, John and Jacob, Riko and Tsakalidis, Konstantinos},
title =	{{External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms}},
booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
pages =	{60:1--60:14},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-124-5},
ISSN =	{1868-8969},
year =	{2019},
volume =	{144},
editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.60},
URN =		{urn:nbn:de:0030-drops-111817},
doi =		{10.4230/LIPIcs.ESA.2019.60},
annote =	{Keywords: priority queues, external memory, graph algorithms, shortest paths, depth-first search, breadth-first search}
}```
Document
Complete Volume
##### OASIcs, Volume 5, ATMOS'06, Complete Volume

Authors: Riko Jacob and Matthias Müller-Hannemann

Published in: OASIcs, Volume 5, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06) (2006)

##### Abstract
OASIcs, Volume 5, ATMOS'06, Complete Volume

##### Cite as

6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06). Open Access Series in Informatics (OASIcs), Volume 5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

```@Proceedings{jacob_et_al:OASIcs.ATMOS.2006,
title =	{{OASIcs, Volume 5, ATMOS'06, Complete Volume}},
booktitle =	{6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06)},
series =	{Open Access Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-01-9},
ISSN =	{2190-6807},
year =	{2012},
volume =	{5},
editor =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2006},
URN =		{urn:nbn:de:0030-drops-35675},
doi =		{10.4230/OASIcs.ATMOS.2006},
annote =	{Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Graph Theory, Applications}
}```
Document
##### 11. Multistage Methods for Freight Train Classification

Authors: Riko Jacob, Peter Marton, Jens Maue, and Marc Nunkesser

Published in: OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

##### Abstract
In this paper we establish a consistent encoding of freight train classification methods. This encoding scheme presents a powerful tool for efficient presentation and analysis of classification methods, which we successfully apply to illustrate the most relevant historic results from a more theoretical point of view. We analyze their performance precisely and develop new classification methods making use of the inherent optimality condition of the encoding. We conclude with deriving optimal algorithms and complexity results for restricted real-world settings.

##### Cite as

Riko Jacob, Peter Marton, Jens Maue, and Marc Nunkesser. 11. Multistage Methods for Freight Train Classification. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 158-174, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

```@InProceedings{jacob_et_al:OASIcs.ATMOS.2007.1179,
author =	{Jacob, Riko and Marton, Peter and Maue, Jens and Nunkesser, Marc},
title =	{{11. Multistage Methods for Freight Train Classification}},
booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
pages =	{158--174},
series =	{Open Access Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-04-0},
ISSN =	{2190-6807},
year =	{2007},
volume =	{7},
editor =	{Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1179},
URN =		{urn:nbn:de:0030-drops-11798},
doi =		{10.4230/OASIcs.ATMOS.2007.1179},
annote =	{Keywords: Freight trains, sorting algorithms, train classification, shunting, cargo}
}```
Document
Front Matter
##### ATMOS 2006 Preface -- Algorithmic Methods and Models for Optimization of Railways

Authors: Riko Jacob and Matthias Müller-Hannemann

Published in: OASIcs, Volume 5, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06) (2006)

##### Abstract
The 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 06) is held on September 14, 2006 in Z{\"u}rich, Switzerland (http://algo06.inf.ethz.ch/atmos), as part of the ALGO meeting.

##### Cite as

6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06). Open Access Series in Informatics (OASIcs), Volume 5, pp. i-v, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

```@InProceedings{jacob_et_al:OASIcs.ATMOS.2006.690,
author =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
title =	{{ATMOS 2006 Preface -- Algorithmic Methods and Models for Optimization of Railways}},
booktitle =	{6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06)},
pages =	{i--v},
series =	{Open Access Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-01-9},
ISSN =	{2190-6807},
year =	{2006},
volume =	{5},
editor =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2006.690},
URN =		{urn:nbn:de:0030-drops-6909},
doi =		{10.4230/OASIcs.ATMOS.2006.690},
annote =	{Keywords: Railway Optimization, Algorithmic Methods, Models}
}```
Document
##### ATMOS 2006 Abstracts Collection -- Presentations at the 6th Workshop on Algorithmic Methods and Models for Optimization of Railways

Authors: Riko Jacob and Matthias Müller-Hannemann

Published in: OASIcs, Volume 5, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06) (2006)

##### Abstract
The 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 06) is held on September 14, 2006 in ZÃƒÂ¼rich, Switzerland (http://algo06.inf.ethz.ch/atmos), as part of the ALGO meeting.

##### Cite as

Riko Jacob and Matthias Müller-Hannemann. ATMOS 2006 Abstracts Collection -- Presentations at the 6th Workshop on Algorithmic Methods and Models for Optimization of Railways. In 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06). Open Access Series in Informatics (OASIcs), Volume 5, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

```@InProceedings{jacob_et_al:OASIcs.ATMOS.2006.689,
author =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
title =	{{ATMOS 2006 Abstracts Collection -- Presentations at the 6th Workshop on Algorithmic Methods and Models for Optimization of Railways}},
booktitle =	{6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06)},
pages =	{1--4},
series =	{Open Access Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-01-9},
ISSN =	{2190-6807},
year =	{2006},
volume =	{5},
editor =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2006.689},
URN =		{urn:nbn:de:0030-drops-6898},
doi =		{10.4230/OASIcs.ATMOS.2006.689},
annote =	{Keywords: Algorithmic Methods and Models for Optimization of Railways, ATMOS}
}```
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