7 Search Results for "Chowdhury, Rezaul A."


Document
Engineering Algorithms for Dynamic Greedy Set Cover

Authors: Amitai Uzrad

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)


Abstract
In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks - such as [GKKP(STOC'17); SU(STOC'23); SUZ(FOCS'24)] - which we simplify by identifying and modifying intricate subroutines that optimize asymptotic bounds but hinder practical performance. We evaluate these algorithms based on solution quality (set cover size) and efficiency, which comprises update time - the time required to update the solution following each insertion/deletion - and recourse - the number of changes made to the solution per update. Each algorithm uses a parameter β to balance quality against efficiency; we investigate the influence of this tradeoff parameter on each algorithm and then perform a comparative analysis to evaluate the algorithms against each other. Our results provide the first practical insights into which algorithmic strategies provide the most value in realistic scenarios.

Cite as

Amitai Uzrad. Engineering Algorithms for Dynamic Greedy Set Cover. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{uzrad:LIPIcs.SEA.2026.26,
  author =	{Uzrad, Amitai},
  title =	{{Engineering Algorithms for Dynamic Greedy Set Cover}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.26},
  URN =		{urn:nbn:de:0030-drops-260308},
  doi =		{10.4230/LIPIcs.SEA.2026.26},
  annote =	{Keywords: Dynamic graphs, set cover, recourse}
}
Document
Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs

Authors: Mridul Ahi, Keerti Choudhary, Shlok Pande, Pushpraj, and Lakshay Saggi

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)


Abstract
This paper addresses the problem of designing fault-tolerant data structures for the (s,t)-max-flow and (s,t)-min-cut problems in unweighted directed graphs. Given a directed graph G = (V, E) with a designated source s, sink t, and an (s,t)-max-flow of value λ, we present constructions for max-flow and min-cut sensitivity oracles, and introduce the concept of a fault-tolerant flow family, which may be of independent interest. Our main contributions are as follows. 1) Fault-Tolerant Flow Family: We construct a family ℬ of 2λ+1 (s,t)-flows such that for every edge e, ℬ contains an (s,t)-max-flow of G-e. This covering property is tight up to constants for single failures and provably cannot extend to comparably small families for k ≥ 2, where we show an Ω(n) lower bound on the family size, independent of λ. 2) Max-Flow Sensitivity Oracle: Using the fault-tolerant flow family, we construct a single as well as dual-edge sensitivity oracle for (s,t)-max-flow that requires only O(λ n) space. Given any set F of up to two failing edges, the oracle reports the updated max-flow value in G-F in O(n) time. Additionally, for the single-failure case, the oracle can determine in constant time whether the flow through an edge x changes when another edge e fails. 3) Min-Cut Sensitivity Oracle for Dual Failures: Recently, Baswana et al. (ICALP’22) designed an O(n²)-sized oracle for answering (s,t)-min-cut size queries under dual edge failures in constant time, along with a matching lower bound. We extend this by focusing on graphs with small min-cut values λ, and present a more compact oracle of size O(λ n) that answers such min-cut size queries in constant time and reports the corresponding (s,t)-min-cut partition in O(n) time. We also show that the space complexity of our oracle is asymptotically optimal in this setting. 4) Min-Cut Sensitivity Oracle for Multiple Failures: We extend our results to the general case of k edge failures. For any graph with (s,t)-min-cut of size λ, we construct a k-fault-tolerant min-cut oracle with space complexity O_{λ,k}(n log n) that answers min-cut size queries in O_{λ,k}(log n) time. This also leads to improved fault-tolerant (s,t)-reachability oracles, achieving O(n log n) space and O(log n) query time for up to k = O(1) edge failures.

Cite as

Mridul Ahi, Keerti Choudhary, Shlok Pande, Pushpraj, and Lakshay Saggi. Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{ahi_et_al:LIPIcs.ITCS.2026.5,
  author =	{Ahi, Mridul and Choudhary, Keerti and Pande, Shlok and Pushpraj and Saggi, Lakshay},
  title =	{{Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.5},
  URN =		{urn:nbn:de:0030-drops-252920},
  doi =		{10.4230/LIPIcs.ITCS.2026.5},
  annote =	{Keywords: Fault tolerance, Data structures, Minimum cuts, Maximum flows}
}
Document
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)


Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.

Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
Vantage Point Selection Algorithms for Bottleneck Capacity Estimation

Authors: Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)


Abstract
Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph G = (V, E) whose edges E have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex v ∈ V, along shortest paths from v to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select k vantage points from V that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all k vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a 1-1/e approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of k tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.

Cite as

Vikrant Ashvinkumar, Rezaul Chowdhury, Jie Gao, Mayank Goswami, Joseph S. B. Mitchell, and Valentin Polishchuk. Vantage Point Selection Algorithms for Bottleneck Capacity Estimation. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{ashvinkumar_et_al:LIPIcs.WADS.2025.6,
  author =	{Ashvinkumar, Vikrant and Chowdhury, Rezaul and Gao, Jie and Goswami, Mayank and Mitchell, Joseph S. B. and Polishchuk, Valentin},
  title =	{{Vantage Point Selection Algorithms for Bottleneck Capacity Estimation}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.6},
  URN =		{urn:nbn:de:0030-drops-242376},
  doi =		{10.4230/LIPIcs.WADS.2025.6},
  annote =	{Keywords: Bottleneck capacity, Approximation algorithms, Instance optimality}
}
Document
On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms

Authors: Lorenzo De Stefani and Vedant Gupta

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)


Abstract
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms, including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary search trees. Assuming no recomputation of intermediate values, we establish an Ω(n³/(√M B)) I/O lower bound, where n denotes the size of the input and M denotes the size of the available fast memory (cache). When recomputation is allowed, we show that the same bound holds for M < cn, where c is a positive constant. In the case where M ≥ 2n, we show an Ω(n/B) I/O lower bound. We also discuss algorithms for which the number of executed I/O operations matches asymptotically each of the presented lower bounds, which are thus asymptotically tight. Additionally, we refine our general method to obtain a lower bound for the I/O complexity of the Cocke-Younger-Kasami algorithm, where the size of the grammar impacts the I/O complexity. An upper bound with asymptotically matching performance in many cases is also provided.

Cite as

Lorenzo De Stefani and Vedant Gupta. On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{destefani_et_al:LIPIcs.WADS.2025.49,
  author =	{De Stefani, Lorenzo and Gupta, Vedant},
  title =	{{On the I/O Complexity of the Cocke-Younger-Kasami Algorithm and of a Family of Related Dynamic Programming Algorithms}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{49:1--49:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.49},
  URN =		{urn:nbn:de:0030-drops-242800},
  doi =		{10.4230/LIPIcs.WADS.2025.49},
  annote =	{Keywords: I/O complexity, Dynamic Programming Algorithms, Lower Bounds, Recomputation, Cocke-Younger-Kasami}
}
Document
Track A: Algorithms, Complexity and Games
Undirected 3-Fault Replacement Path in Nearly Cubic Time

Authors: Shucheng Chi, Ran Duan, Benyu Wang, and Tianle Xie

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)


Abstract
Given a graph G = (V,E) (n = |V|, m = |E|) and two vertices s,t ∈ V, the f-fault replacement path (fFRP) problem computes for every set F of at most f edges, the distance from s to t when edges in F fail. A recent result shows that 2FRP in directed graphs can be solved in Õ(n³) time [Vassilevska Williams, Woldeghebriel, Xu 2022]. In this paper, we show a 3FRP algorithm in deterministic Õ(n³) time for undirected weighted graphs, which almost matches the size of the output. This implies that fFRP in undirected graphs can be solved in nearly optimal Õ(n^f) time for all f ≥ 3. To construct our 3FRP algorithm, we introduce an incremental distance sensitivity oracle (DSO) for undirected graphs with Õ(n²) worst-case update time, while preprocessing time, space, and query time are still Õ(n³), Õ(n²) and Õ(1), respectively, which match the static DSO [Bernstein and Karger 2009]. Here in a DSO, we can preprocess a graph so that the distance between any pair of vertices given any failed edge can be answered efficiently. From the recent result in [Peng and Rubinstein 2023], we can obtain an offline dynamic DSO from the incremental worst-case DSO, which makes the construction of our 3FRP algorithm more convenient. By the offline dynamic DSO, we can also construct a 2-fault single-source replacement path (2-fault SSRP) algorithm in Õ(n³) time, that is, from a given vertex s, we want to find the distance to any vertex t when any pair of edges fail. Thus the Õ(n³) time complexity for 2-fault SSRP is also nearly optimal. Now we know that in undirected graphs 1FRP can be solved in Õ(m) time [Nardelli, Proietti, Widmayer 2001], and 2FRP and 3FRP in undirected graphs can be solved in Õ(n³) time. In this paper, we also show that a truly subcubic algorithm for 2FRP in undirected weighted graphs does not exist under APSP hypothesis.

Cite as

Shucheng Chi, Ran Duan, Benyu Wang, and Tianle Xie. Undirected 3-Fault Replacement Path in Nearly Cubic Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 57:1-57:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{chi_et_al:LIPIcs.ICALP.2025.57,
  author =	{Chi, Shucheng and Duan, Ran and Wang, Benyu and Xie, Tianle},
  title =	{{Undirected 3-Fault Replacement Path in Nearly Cubic Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{57:1--57:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.57},
  URN =		{urn:nbn:de:0030-drops-234346},
  doi =		{10.4230/LIPIcs.ICALP.2025.57},
  annote =	{Keywords: Graph Algorithm, Shortest Path, Replacement Path}
}
Document
When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting

Authors: Arghya Bhattacharya, Abiyaz Chowdhury, Helen Xu, Rathish Das, Rezaul A. Chowdhury, Rob Johnson, Rishab Nithyanand, and Michael A. Bender

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


Abstract
Cache-adaptive algorithms are a class of algorithms that achieve optimal utilization of dynamically changing memory. These memory fluctuations are the norm in today’s multi-threaded shared-memory machines and time-sharing caches. Bender et al. [Bender et al., 2014] proved that many cache-oblivious algorithms are optimally cache-adaptive, but that some cache-oblivious algorithms can be relatively far from optimally cache-adaptive on worst-case memory fluctuations. This worst-case gap between cache obliviousness and cache adaptivity depends on a highly-structured, adversarial memory profile. Existing cache-adaptive analysis does not predict the relative performance of cache-oblivious and cache-adaptive algorithms on non-adversarial profiles. Does the worst-case gap appear in practice, or is it an artifact of an unrealistically powerful adversary? This paper sheds light on the question of whether cache-oblivious algorithms can effectively adapt to realistically fluctuating memory sizes; the paper focuses on matrix multiplication and sorting. The two matrix-multiplication algorithms in this paper are canonical examples of "(a, b, c)-regular" cache-oblivious algorithms, which underlie much of the existing theory on cache-adaptivity. Both algorithms have the same asymptotic I/O performance when the memory size remains fixed, but one is optimally cache-adaptive, and the other is not. In our experiments, we generate both adversarial and non-adversarial memory workloads. The performance gap between the algorithms for matrix multiplication grows with problem size (up to 3.8×) on the adversarial profiles, but the gap does not grow with problem size (stays at 2×) on non-adversarial profiles. The sorting algorithms in this paper are not "(a, b, c)-regular," but they have been well-studied in the classical external-memory model when the memory size does not fluctuate. The relative performance of a non-oblivious (cache-aware) sorting algorithm degrades with the problem size: it incurs up to 6 × the number of disk I/Os compared to an oblivious adaptive algorithm on both adversarial and non-adversarial profiles. To summarize, in all our experiments, the cache-oblivious matrix-multiplication and sorting algorithms that we tested empirically adapt well to memory fluctuations. We conjecture that cache-obliviousness will empirically help achieve adaptivity for other problems with similar structures.

Cite as

Arghya Bhattacharya, Abiyaz Chowdhury, Helen Xu, Rathish Das, Rezaul A. Chowdhury, Rob Johnson, Rishab Nithyanand, and Michael A. Bender. When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bhattacharya_et_al:LIPIcs.ESA.2022.16,
  author =	{Bhattacharya, Arghya and Chowdhury, Abiyaz and Xu, Helen and Das, Rathish and Chowdhury, Rezaul A. and Johnson, Rob and Nithyanand, Rishab and Bender, Michael A.},
  title =	{{When Are Cache-Oblivious Algorithms Cache Adaptive? A Case Study of Matrix Multiplication and Sorting}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{16:1--16:17},
  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.2022.16},
  URN =		{urn:nbn:de:0030-drops-169543},
  doi =		{10.4230/LIPIcs.ESA.2022.16},
  annote =	{Keywords: Cache-adaptive algorithms, cache-oblivious algorithms}
}
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