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Documents authored by Bansal, Ishan

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.20
Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity

Authors: Ishan Bansal, Joe Cheriyan, Sanjeev Khanna, and Miles Simmons

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

Abstract
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-k-ECSS problem, we are given a graph G = (V,E) whose edges have non-negative costs and positive integer capacities, and the goal is to find a minimum-cost edge-set F such that every non-trivial cut of the graph G' = (V,F) has capacity at least k. Let n = |V| and let u_{min} (respectively, u_{max}) denote the minimum (respectively, maximum) capacity of an edge; assume that u_{max} ≤ k. We present an O(log({k}/u_{min}))-approximation algorithm for the Cap-k-ECSS problem, asymptotically improving upon the previous best approximation ratio of min(O(log{n}), k, 2u_{max}, 6 ⋅ {⌈ k/u_{min} ⌉}) whenever log(k/u_{min}) = o(log{n}) and u_{max} is sufficiently large. In the (p,q)-Flexible Graph Connectivity problem, denoted (p,q)-FGC, the input is a graph G = (V, E) where E is partitioned into safe and unsafe edges, and the goal is to find a minimum-cost edge-set F such that the subgraph G' = (V, F) remains p-edge connected upon removal of any q unsafe edges from F. We present an 8-approximation algorithm for the (1,q)-FGC problem that improves upon the previous best approximation ratio of (q+1). Both of our results are obtained by using natural LP relaxations strengthened with the knapsack-cover inequalities, and then, during the rounding process, utilizing a recent O(1)-approximation algorithm for the Cover Small Cuts problem. In the latter problem, the goal is to find a minimum-cost set of links such that each non-trivial cut of capacity less than a specified value is covered by a link. We also show that the problem of covering small cuts inherently arises in another variant of (p,q)-FGC. Specifically, we give Cook reductions that preserve approximation ratios within O(1) factors between the (2,q)-FGC problem and the 2-Cover Small Cuts problem; in the latter problem, each small cut needs to be covered by two links.
Cite as

Ishan Bansal, Joe Cheriyan, Sanjeev Khanna, and Miles Simmons. Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bansal_et_al:LIPIcs.ICALP.2025.20,
  author =	{Bansal, Ishan and Cheriyan, Joe and Khanna, Sanjeev and Simmons, Miles},
  title =	{{Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{20:1--20:20},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-233973},
  doi =		{10.4230/LIPIcs.ICALP.2025.20},
  annote =	{Keywords: Approximation algorithms, Capacitated network design, Covering small cuts, Edge-connectivity of graphs, f-Connectivity problem, Flexible Graph Connectivity, Knapsack-cover inequalities}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.14
Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals

Authors: Ishan Bansal, Joe Cheriyan, Logan Grout, and Sharat Ibrahimpur

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
The k-Steiner-2NCS problem is as follows: Given a constant (positive integer) k, and an undirected connected graph G = (V,E), non-negative costs c on the edges, and a partition (T, V⧵T) of V into a set of terminals, T, and a set of non-terminals (or, Steiner nodes), where |T| = k, find a min-cost two-node connected subgraph that contains the terminals. The k-Steiner-2ECS problem has the same inputs; the algorithmic goal is to find a min-cost two-edge connected subgraph that contains the terminals. We present a randomized polynomial-time algorithm for the unweighted k-Steiner-2NCS problem, and a randomized FPTAS for the weighted k-Steiner-2NCS problem. We obtain similar results for a capacitated generalization of the k-Steiner-2ECS problem. Our methods build on results by Björklund, Husfeldt, and Taslaman (SODA 2012) that give a randomized polynomial-time algorithm for the unweighted k-Steiner-cycle problem; this problem has the same inputs as the unweighted k-Steiner-2NCS problem, and the algorithmic goal is to find a min-cost simple cycle C that contains the terminals (C may contain any number of Steiner nodes).
Cite as

Ishan Bansal, Joe Cheriyan, Logan Grout, and Sharat Ibrahimpur. Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bansal_et_al:LIPIcs.APPROX/RANDOM.2023.14,
  author =	{Bansal, Ishan and Cheriyan, Joe and Grout, Logan and Ibrahimpur, Sharat},
  title =	{{Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.14},
  URN =		{urn:nbn:de:0030-drops-188396},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.14},
  annote =	{Keywords: Approximation algorithms, Capacitated network design, Network design, Parametrized algorithms, Steiner cycle problem, Steiner 2-edge connected subgraphs, Steiner 2-node connected subgraphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.15
Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions

Authors: Ishan Bansal, Joseph Cheriyan, Logan Grout, and Sharat Ibrahimpur

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Combinatorica 15(3):435-454, 1995). Williamson et al. prove an approximation ratio of two for connectivity augmentation problems where the connectivity requirements can be specified by uncrossable functions. They state: "Extending our algorithm to handle non-uncrossable functions remains a challenging open problem. The key feature of uncrossable functions is that there exists an optimal dual solution which is laminar... A larger open issue is to explore further the power of the primal-dual approach for obtaining approximation algorithms for other combinatorial optimization problems." Our main result proves a 16-approximation ratio via the primal-dual method for a class of functions that generalizes the notion of an uncrossable function. There exist instances that can be handled by our methods where none of the optimal dual solutions have a laminar support. We present applications of our main result to three network-design problems. 1) A 16-approximation algorithm for augmenting the family of small cuts of a graph G. The previous best approximation ratio was O(log |V(G)|). 2) A 16⋅⌈k/u_min⌉-approximation algorithm for the Cap-k-ECSS problem which is as follows: Given an undirected graph G = (V,E) with edge costs c ∈ ℚ_{≥0}^E and edge capacities u ∈ ℤ_{≥0}^E, find a minimum cost subset of the edges F ⊆ E such that the capacity across any cut in (V,F) is at least k; u_min (respectively, u_max) denote the minimum (respectively, maximum) capacity of an edge in E, and w.l.o.g. u_max ≤ k. The previous best approximation ratio was min(O(log|V|), k, 2u_max). 3) A 20-approximation algorithm for the model of (p,2)-Flexible Graph Connectivity. The previous best approximation ratio was O(log|V(G)|), where G denotes the input graph.
Cite as

Ishan Bansal, Joseph Cheriyan, Logan Grout, and Sharat Ibrahimpur. Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bansal_et_al:LIPIcs.ICALP.2023.15,
  author =	{Bansal, Ishan and Cheriyan, Joseph and Grout, Logan and Ibrahimpur, Sharat},
  title =	{{Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.15},
  URN =		{urn:nbn:de:0030-drops-180678},
  doi =		{10.4230/LIPIcs.ICALP.2023.15},
  annote =	{Keywords: Approximation algorithms, Edge-connectivity of graphs, f-Connectivity problem, Flexible Graph Connectivity, Minimum cuts, Network design, Primal-dual method, Small cuts}
}
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