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Documents authored by Das, Syamantak

Document
DOI: 10.4230/LIPIcs.MFCS.2024.45
Nearly-Tight Bounds for Flow Sparsifiers in Quasi-Bipartite Graphs

Authors: Syamantak Das, Nikhil Kumar, and Daniel Vaz

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Flow sparsification is a classic graph compression technique which, given a capacitated graph G on k terminals, aims to construct another capacitated graph H, called a flow sparsifier, that preserves, either exactly or approximately, every multicommodity flow between terminals (ideally, with size as a small function of k). Cut sparsifiers are a restricted variant of flow sparsifiers which are only required to preserve maximum flows between bipartitions of the terminal set. It is known that exact cut sparsifiers require 2^Ω(k) many vertices [Krauthgamer and Rika, SODA 2013], with the hard instances being quasi-bipartite graphs, where there are no edges between non-terminals. On the other hand, it has been shown recently that exact (or even (1+ε)-approximate) flow sparsifiers on networks with just 6 terminals require unbounded size [Krauthgamer and Mosenzon, SODA 2023, Chen and Tan, SODA 2024]. In this paper, we construct exact flow sparsifiers of size 3^k³ and exact cut sparsifiers of size 2^k² for quasi-bipartite graphs. In particular, the flow sparsifiers are contraction-based, that is, they are obtained from the input graph by (vertex) contraction operations. Our main contribution is a new technique to construct sparsifiers that exploits connections to polyhedral geometry, and that can be generalized to graphs with a small separator that separates the graph into small components. We also give an improved reduction theorem for graphs of bounded treewidth [Andoni et al., SODA 2011], implying a flow sparsifier of size O(k⋅w) and quality O((log w)/log log w), where w is the treewidth.
Cite as

Syamantak Das, Nikhil Kumar, and Daniel Vaz. Nearly-Tight Bounds for Flow Sparsifiers in Quasi-Bipartite Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{das_et_al:LIPIcs.MFCS.2024.45,
  author =	{Das, Syamantak and Kumar, Nikhil and Vaz, Daniel},
  title =	{{Nearly-Tight Bounds for Flow Sparsifiers in Quasi-Bipartite Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{45:1--45:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.45},
  URN =		{urn:nbn:de:0030-drops-206018},
  doi =		{10.4230/LIPIcs.MFCS.2024.45},
  annote =	{Keywords: Graph Sparsification, Cut Sparsifiers, Flow Sparsifiers, Quasi-bipartite Graphs, Bounded Treewidth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.40
A Simpler QPTAS for Scheduling Jobs with Precedence Constraints

Authors: Syamantak Das and Andreas Wiese

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study the classical scheduling problem of minimizing the makespan of a set of unit size jobs with precedence constraints on parallel identical machines. Research on the problem dates back to the landmark paper by Graham from 1966 who showed that the simple List Scheduling algorithm is a (2-1/m)-approximation. Interestingly, it is open whether the problem is NP-hard if m = 3 which is one of the few remaining open problems in the seminal book by Garey and Johnson. Recently, quite some progress has been made for the setting that m is a constant. In a break-through paper, Levey and Rothvoss presented a (1+ε)-approximation with a running time of n^{(log n)^{O((m²/ε²)log log n)}} [STOC 2016, SICOMP 2019] and this running time was improved to quasi-polynomial by Garg [ICALP 2018] and to even n^O_{m,ε}(log³log n) by Li [SODA 2021]. These results use techniques like LP-hierarchies, conditioning on certain well-selected jobs, and abstractions like (partial) dyadic systems and virtually valid schedules. In this paper, we present a QPTAS for the problem which is arguably simpler than the previous algorithms. We just guess the positions of certain jobs in the optimal solution, recurse on a set of guessed subintervals, and fill in the remaining jobs with greedy routines. We believe that also our analysis is more accessible, in particular since we do not use (LP-)hierarchies or abstractions of the problem like the ones above, but we guess properties of the optimal solution directly.
Cite as

Syamantak Das and Andreas Wiese. A Simpler QPTAS for Scheduling Jobs with Precedence Constraints. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 40:1-40:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{das_et_al:LIPIcs.ESA.2022.40,
  author =	{Das, Syamantak and Wiese, Andreas},
  title =	{{A Simpler QPTAS for Scheduling Jobs with Precedence Constraints}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{40:1--40:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.40},
  URN =		{urn:nbn:de:0030-drops-169782},
  doi =		{10.4230/LIPIcs.ESA.2022.40},
  annote =	{Keywords: makespan minimization, precedence constraints, QPTAS}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.55
A Constant Factor Approximation for Capacitated Min-Max Tree Cover

Authors: Syamantak Das, Lavina Jain, and Nikhil Kumar

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
Given a graph G = (V,E) with non-negative real edge lengths and an integer parameter k, the (uncapacitated) Min-Max Tree Cover problem seeks to find a set of at most k trees which together span V and each tree is a subgraph of G. The objective is to minimize the maximum length among all the trees. In this paper, we consider a capacitated generalization of the above and give the first constant factor approximation algorithm. In the capacitated version, there is a hard uniform capacity (λ) on the number of vertices a tree can cover. Our result extends to the rooted version of the problem, where we are given a set of k root vertices, R and each of the covering trees is required to include a distinct vertex in R as the root. Prior to our work, the only result known was a (2k-1)-approximation algorithm for the special case when the total number of vertices in the graph is kλ [Guttmann-Beck and Hassin, J. of Algorithms, 1997]. Our technique circumvents the difficulty of using the minimum spanning tree of the graph as a lower bound, which is standard for the uncapacitated version of the problem [Even et al.,OR Letters 2004] [Khani et al.,Algorithmica 2010]. Instead, we use Steiner trees that cover λ vertices along with an iterative refinement procedure that ensures that the output trees have low cost and the vertices are well distributed among the trees.
Cite as

Syamantak Das, Lavina Jain, and Nikhil Kumar. A Constant Factor Approximation for Capacitated Min-Max Tree Cover. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 55:1-55:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{das_et_al:LIPIcs.APPROX/RANDOM.2020.55,
  author =	{Das, Syamantak and Jain, Lavina and Kumar, Nikhil},
  title =	{{A Constant Factor Approximation for Capacitated Min-Max Tree Cover}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{55:1--55:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.55},
  URN =		{urn:nbn:de:0030-drops-126581},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.55},
  annote =	{Keywords: Approximation Algorithms, Graph Algorithms, Min-Max Tree Cover, Vehicle Routing, Steiner Tree}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.8
Survivable Network Design for Group Connectivity in Low-Treewidth Graphs

Authors: Parinya Chalermsook, Syamantak Das, Guy Even, Bundit Laekhanukit, and Daniel Vaz

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
In the Group Steiner Tree problem (GST), we are given a (edge or vertex)-weighted graph G=(V,E) on n vertices, together with a root vertex r and a collection of groups {S_i}_{i in [h]}: S_i subseteq V(G). The goal is to find a minimum-cost subgraph H that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each group S_i has a demand k_i in [k], k in N, and we wish to find a minimum-cost subgraph H subseteq G such that, for each group S_i, there is a vertex in the group that is connected to the root via k_i (vertex or edge) disjoint paths. While GST admits O(log^2 n log h) approximation, its higher connectivity variants are known to be Label-Cover hard, and for the vertex-weighted version, the hardness holds even when k=2 (it is widely believed that there is no subpolynomial approximation for the Label-Cover problem [Bellare et al., STOC 1993]). More precisely, the problem admits no 2^{log^{1-epsilon}n}-approximation unless NP subseteq DTIME(n^{polylog(n)}). Previously, positive results were known only for the edge-weighted version when k=2 [Gupta et al., SODA 2010; Khandekar et al., Theor. Comput. Sci., 2012] and for a relaxed variant where k_i disjoint paths from r may end at different vertices in a group [Chalermsook et al., SODA 2015], for which the authors gave a bicriteria approximation. For k >= 3, there is no non-trivial approximation algorithm known for edge-weighted Restricted Group SNDP, except for the special case of the relaxed variant on trees (folklore). Our main result is an O(log n log h) approximation algorithm for Restricted Group SNDP that runs in time n^{f(k, w)}, where w is the treewidth of the input graph. Our algorithm works for both edge and vertex weighted variants, and the approximation ratio nearly matches the lower bound when k and w are constants. The key to achieving this result is a non-trivial extension of a framework introduced in [Chalermsook et al., SODA 2017]. This framework first embeds all feasible solutions to the problem into a dynamic program (DP) table. However, finding the optimal solution in the DP table remains intractable. We formulate a linear program relaxation for the DP and obtain an approximate solution via randomized rounding. This framework also allows us to systematically construct DP tables for high-connectivity problems. As a result, we present new exact algorithms for several variants of survivable network design problems in low-treewidth graphs.
Cite as

Parinya Chalermsook, Syamantak Das, Guy Even, Bundit Laekhanukit, and Daniel Vaz. Survivable Network Design for Group Connectivity in Low-Treewidth Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chalermsook_et_al:LIPIcs.APPROX-RANDOM.2018.8,
  author =	{Chalermsook, Parinya and Das, Syamantak and Even, Guy and Laekhanukit, Bundit and Vaz, Daniel},
  title =	{{Survivable Network Design for Group Connectivity in Low-Treewidth Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.8},
  URN =		{urn:nbn:de:0030-drops-94127},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.8},
  annote =	{Keywords: Approximation Algorithms, Hardness of Approximation, Survivable Network Design, Group Steiner Tree}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.31
On Minimizing the Makespan When Some Jobs Cannot Be Assigned on the Same Machine

Authors: Syamantak Das and Andreas Wiese

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We study the classical scheduling problem of assigning jobs to machines in order to minimize the makespan. It is well-studied and admits an EPTAS on identical machines and a (2-1/m)-approximation algorithm on unrelated machines. In this paper we study a variation in which the input jobs are partitioned into bags and no two jobs from the same bag are allowed to be assigned on the same machine. Such a constraint can easily arise, e.g., due to system stability and redundancy considerations. Unfortunately, as we demonstrate in this paper, the techniques of the above results break down in the presence of these additional constraints. Our first result is a PTAS for the case of identical machines. It enhances the methods from the known (E)PTASs by a finer classification of the input jobs and careful argumentations why a good schedule exists after enumerating over the large jobs. For unrelated machines, we prove that there can be no (log n)^{1/4-epsilon}-approximation algorithm for the problem for any epsilon > 0, assuming that NP nsubseteq ZPTIME(2^{(log n)^{O(1)}}). This holds even in the restricted assignment setting. However, we identify a special case of the latter in which we can do better: if the same set of machines we give an 8-approximation algorithm. It is based on rounding the LP-relaxation of the problem in phases and adjusting the residual fractional solution after each phase to order to respect the bag constraints.
Cite as

Syamantak Das and Andreas Wiese. On Minimizing the Makespan When Some Jobs Cannot Be Assigned on the Same Machine. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{das_et_al:LIPIcs.ESA.2017.31,
  author =	{Das, Syamantak and Wiese, Andreas},
  title =	{{On Minimizing the Makespan When Some Jobs Cannot Be Assigned on the Same Machine}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.31},
  URN =		{urn:nbn:de:0030-drops-78453},
  doi =		{10.4230/LIPIcs.ESA.2017.31},
  annote =	{Keywords: approximation algorithms, scheduling, makespan minimization}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.25
Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model

Authors: Anamitra Roy Choudhury, Syamantak Das, and Amit Kumar

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
We consider the online scheduling problem to minimize the weighted ell_p-norm of flow-time of jobs. We study this problem under the rejection model introduced by Choudhury et al. (SODA 2015) - here the online algorithm is allowed to not serve an eps-fraction of the requests. We consider the restricted assignments setting where each job can go to a specified subset of machines. Our main result is an immediate dispatch non-migratory 1/eps^{O(1)}-competitive algorithm for this problem when one is allowed to reject at most eps-fraction of the total weight of jobs arriving. This is in contrast with the speed augmentation model under which no online algorithm for this problem can achieve a competitive ratio independent of p.
Cite as

Anamitra Roy Choudhury, Syamantak Das, and Amit Kumar. Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 25-37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{roychoudhury_et_al:LIPIcs.FSTTCS.2015.25,
  author =	{Roy Choudhury, Anamitra and Das, Syamantak and Kumar, Amit},
  title =	{{Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{25--37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.25},
  URN =		{urn:nbn:de:0030-drops-56341},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.25},
  annote =	{Keywords: online scheduling, flow-time, competitive analysis}
}
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