13 Search Results for "Ibrahimpur, Sharat"

Document
DOI: 10.4230/LIPIcs.ESA.2025.38
Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique

Authors: Nikhil Kumar, J. J. Nan, and Chaitanya Swamy

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

Abstract
In the classical survivable-network-design problem (SNDP), we are given an undirected graph G = (V, E), non-negative edge costs, and some k tuples (s_i,t_i,r_i), where s_i,t_i ∈ V and r_i ∈ ℤ_+. The objective is to find a minimum-cost subset H ⊆ E such that each s_i-t_i pair remains connected even after the failure of any r_i-1 edges. It is well-known that SNDP can be equivalently modeled using a weakly-supermodular cut-requirement function f, where the objective is to find the minimum-cost subset of edges that picks at least f(S) edges across every cut S ⊆ V. Recently, motivated by fault-tolerance in graph spanners, Dinitz, Koranteng, and Kortsartz proposed a variant of SNDP that enforces a relative level of fault tolerance with respect to G. Even if a feasible SNDP-solution may not exist due to G lacking the required fault-tolerance, the goal is to find a solution H that is at least as fault-tolerant as G itself. They formalize the latter condition in terms of paths and fault-sets, which gives rise to path-relative SNDP (which they call relative SNDP). Along these lines, we introduce a new model of relative network design, called cut-relative SNDP (CR-SNDP), where the goal is to select a minimum-cost subset of edges that satisfies the given (weakly-supermodular) cut-requirement function to the maximum extent possible, i.e., by picking min{f(S), |δ_G(S)|} edges across every cut S ⊆ V. Unlike SNDP, the cut-relative and path-relative versions of SNDP are not equivalent. The resulting cut-requirement function for CR-SNDP (as also path-relative SNDP) is not weakly supermodular, and extreme-point solutions to the natural LP-relaxation need not correspond to a laminar family of tight cut constraints. Consequently, standard techniques cannot be used directly to design approximation algorithms for this problem. We develop a novel decomposition technique to circumvent this difficulty and use it to give a tight 2-approximation algorithm for CR-SNDP. We also show some new hardness results for these relative-SNDP problems.
Cite as

Nikhil Kumar, J. J. Nan, and Chaitanya Swamy. Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kumar_et_al:LIPIcs.ESA.2025.38,
  author =	{Kumar, Nikhil and Nan, J. J. and Swamy, Chaitanya},
  title =	{{Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{38:1--38:18},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-245061},
  doi =		{10.4230/LIPIcs.ESA.2025.38},
  annote =	{Keywords: Approximation algorithms, Network Design, Cut-requirement functions, Weak Supermodularity, Iterative rounding, LP rounding algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.83
Fault-Tolerant Matroid Bases

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle

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

Abstract
We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid ℳ and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the remaining subset still spans the entire ground set. Since matroids generalize linear independence across structures such as vector spaces, graphs, and set systems, this problem unifies and extends several fault-tolerant concepts appearing in prior research. Our main contribution is a fixed-parameter tractable (FPT) algorithm for the k-fault-tolerant basis problem, parameterized by both k and the rank r of the matroid. This two-variable parameterization by k + r is shown to be tight in the following sense. On the one hand, the problem is already NP-hard for k = 1. On the other hand, it is Para-NP-hard for r ≥ 3 and polynomial-time solvable for r ≤ 2.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle. Fault-Tolerant Matroid Bases. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 83:1-83:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bentert_et_al:LIPIcs.ESA.2025.83,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Morelle, Laure},
  title =	{{Fault-Tolerant Matroid Bases}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{83:1--83:14},
  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.2025.83},
  URN =		{urn:nbn:de:0030-drops-245511},
  doi =		{10.4230/LIPIcs.ESA.2025.83},
  annote =	{Keywords: Parameterized Complexity, matroids, robust bases}
}
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)

Copy BibTex To Clipboard

@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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.50
New Results on a General Class of Minimum Norm Optimization Problems

Authors: Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang

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

Abstract
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set 𝒰 of n weighted elements and a family of feasible subsets ℱ. Each subset S ∈ ℱ is called a feasible solution/set of the problem. We denote the value vector by v = {v_i}_{i ∈ [n]}, where v_i ≥ 0 is the value of element i. For any subset S ⊆ 𝒰, we use v[S] to denote the n-dimensional vector {v_e⋅ 𝟏[e ∈ S]}_{e ∈ 𝒰} (i.e., we zero out all entries that are not in S). Let f: ℝⁿ → ℝ_+ be a symmetric monotone norm function. Our goal is to minimize the norm objective f(v[S]) over feasible subset S ∈ ℱ. The problem significantly generalizes the corresponding min-sum and min-max problems. We present a general equivalent reduction of the norm minimization problem to a multi-criteria optimization problem with logarithmic budget constraints, up to a constant approximation factor. Leveraging this reduction, we obtain constant factor approximation algorithms for the norm minimization versions of several covering problems, such as interval cover, multi-dimensional knapsack cover, and logarithmic factor approximation for set cover. We also study the norm minimization versions for perfect matching, s-t path and s-t cut. We show the natural linear programming relaxations for these problems have a large integrality gap. To complement the negative result, we show that, for perfect matching, it is possible to obtain a bi-criteria result: for any constant ε,δ > 0, we can find in polynomial time a nearly perfect matching (i.e., a matching that matches at least 1-ε proportion of vertices) and its cost is at most (8+δ) times of the optimum for perfect matching. Moreover, we establish the existence of a polynomial-time O(log log n)-approximation algorithm for the norm minimization variant of the s-t path problem. Specifically, our algorithm achieves an α-approximation with a time complexity of n^{O(log log n / α)}, where 9 ≤ α ≤ log log n.
Cite as

Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang. New Results on a General Class of Minimum Norm Optimization Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ICALP.2025.50,
  author =	{Chen, Kuowen and Li, Jian and Rabani, Yuval and Zhang, Yiran},
  title =	{{New Results on a General Class of Minimum Norm Optimization Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{50:1--50:20},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-234276},
  doi =		{10.4230/LIPIcs.ICALP.2025.50},
  annote =	{Keywords: Approximation Algorithms, Minimum Norm Optimization, Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.51
Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures

Authors: Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the (p,q)-Steiner-Connectivity Preservation problem where we protect a minimum-cost set of edges such that the underlying graph maintains p-edge-connectivity between given terminal pairs against edge failures, assuming at most q unprotected edges can fail. We design polynomial-time exact algorithms for the cases where p and q are small and approximation algorithms for general values of p and q. Additionally, we show that when both p and q are part of the input, even deciding whether a given solution is feasible is NP-complete. This hardness also carries over to Flexible Network Design, a research direction that has gained significant attention. In particular, previous work focuses on problem settings where either p or q is constant, for which our new hardness result now provides justification.
Cite as

Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang. Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{hommelsheim_et_al:LIPIcs.STACS.2025.51,
  author =	{Hommelsheim, Felix and Liu, Zhenwei and Megow, Nicole and Zhang, Guochuan},
  title =	{{Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.51},
  URN =		{urn:nbn:de:0030-drops-228761},
  doi =		{10.4230/LIPIcs.STACS.2025.51},
  annote =	{Keywords: Network Design, Edge Failures, Graph Connectivity, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.57
Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously

Authors: Matthias Kaul, Kelin Luo, Matthias Mnich, and Heiko Röglin

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We study the problem of partitioning a set of n objects in a metric space into k clusters V₁,...,V_k. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric norm of that vector (in particular, this includes the 𝓁_p-norms). For the costs of the clusters we take the weight of a minimum-weight spanning tree on the objects in V_i, which may serve as a proxy for the cost of traversing all objects in the cluster, for example in the context of Multirobot Coverage as studied by Zheng, Koenig, Kempe, Jain (IROS 2005), but also as a shape-invariant measure of cluster density similar to Single-Linkage Clustering. This problem has been studied by Even, Garg, Könemann, Ravi, Sinha (Oper. Res. Lett., 2004) for the setting of minimizing the weight of the largest cluster (i.e., using 𝓁_∞) as Min-Max Tree Cover, for which they gave a constant-factor approximation algorithm. We provide a careful adaptation of their algorithm to compute solutions which are approximately optimal with respect to all monotone symmetric norms simultaneously, and show how to find them in polynomial time. In fact, our algorithm is purely combinatorial and can process metric spaces with 10,000 points in less than a second. As an extension, we also consider the case where instead of a target number of clusters we are provided with a set of depots in the space such that every cluster should contain at least one such depot. One can consider these as the fixed starting points of some agents that will traverse all points of a cluster. For this setting also we are able to give a polynomial-time algorithm computing a constant-factor approximation with respect to all monotone symmetric norms simultaneously. To show that the algorithmic results are tight up to the precise constant of approximation attainable, we also prove that such clustering problems are already APX-hard when considering only one single 𝓁_p norm for the objective.
Cite as

Matthias Kaul, Kelin Luo, Matthias Mnich, and Heiko Röglin. Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kaul_et_al:LIPIcs.STACS.2025.57,
  author =	{Kaul, Matthias and Luo, Kelin and Mnich, Matthias and R\"{o}glin, Heiko},
  title =	{{Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{57:1--57:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.57},
  URN =		{urn:nbn:de:0030-drops-228821},
  doi =		{10.4230/LIPIcs.STACS.2025.57},
  annote =	{Keywords: Clustering, spanning trees, all-norm approximation}
}
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)

Copy BibTex To Clipboard

@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)

Copy BibTex To Clipboard

@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}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.80
Efficient Caching with Reserves via Marking

Authors: Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang

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

Abstract
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis - including potential functions and primal-dual techniques - give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [Ibrahimpur et al., 2022] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.
Cite as

Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Efficient Caching with Reserves via Marking. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 80:1-80:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{ibrahimpur_et_al:LIPIcs.ICALP.2023.80,
  author =	{Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.},
  title =	{{Efficient Caching with Reserves via Marking}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{80:1--80:20},
  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.2023.80},
  URN =		{urn:nbn:de:0030-drops-181328},
  doi =		{10.4230/LIPIcs.ICALP.2023.80},
  annote =	{Keywords: Approximation Algorithms, Online Algorithms, Caching}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.52
Caching with Reserves

Authors: Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Caching is among the most well-studied topics in algorithm design, in part because it is such a fundamental component of many computer systems. Much of traditional caching research studies cache management for a single-user or single-processor environment. In this paper, we propose two related generalizations of the classical caching problem that capture issues that arise in a multi-user or multi-processor environment. In the caching with reserves problem, a caching algorithm is required to maintain at least k_i pages belonging to user i in the cache at any time, for some given reserve capacities k_i. In the public-private caching problem, the cache of total size k is partitioned into subcaches, a private cache of size k_i for each user i and a shared public cache usable by any user. In both of these models, as in the classical caching framework, the objective of the algorithm is to dynamically maintain the cache so as to minimize the total number of cache misses. We show that caching with reserves and public-private caching models are equivalent up to constant factors, and thus focus on the former. Unlike classical caching, both of these models turn out to be NP-hard even in the offline setting, where the page sequence is known in advance. For the offline setting, we design a 2-approximation algorithm, whose analysis carefully keeps track of a potential function to bound the cost. In the online setting, we first design an O(ln k)-competitive fractional algorithm using the primal-dual framework, and then show how to convert it online to a randomized integral algorithm with the same guarantee.
Cite as

Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Caching with Reserves. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 52:1-52:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ibrahimpur_et_al:LIPIcs.APPROX/RANDOM.2022.52,
  author =	{Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.},
  title =	{{Caching with Reserves}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{52:1--52:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.52},
  URN =		{urn:nbn:de:0030-drops-171741},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.52},
  annote =	{Keywords: Approximation Algorithms, Online Algorithms, Caching}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.9
Approximation Algorithms for Flexible Graph Connectivity

Authors: Sylvia Boyd, Joseph Cheriyan, Arash Haddadan, and Sharat Ibrahimpur

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and Mühlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), IPCO 2020: pp. 13-26). In an instance of the Flexible Graph Connectivity (FGC) problem, we have an undirected connected graph G = (V,E), a partition of E into a set of safe edges S and a set of unsafe edges U, and nonnegative costs {c_e}_{e ∈ E} on the edges. A subset F ⊆ E of edges is feasible for FGC if for any unsafe edge e ∈ F ∩ U, the subgraph (V,F⧵{e}) is connected. The algorithmic goal is to find a (feasible) solution F that minimizes c(F) = ∑_{e ∈ F} c_e. We present a simple 2-approximation algorithm for FGC via a reduction to the minimum-cost r-out 2-arborescence problem. This improves upon the 2.527-approximation algorithm of Adjiashvili et al. For integers p ≥ 1 and q ≥ 0, the (p,q)-FGC problem is a generalization of FGC where we seek a minimum-cost subgraph H = (V,F) that remains p-edge connected against the failure of any set of at most q unsafe edges; that is, for any set F' ⊆ U with |F'| ≤ q, H-F' = (V, F ⧵ F') should be p-edge connected. Note that FGC corresponds to the (1,1)-FGC problem. We give approximation algorithms for two important special cases of (p,q)-FGC: (a) Our 2-approximation algorithm for FGC extends to a (k+1)-approximation algorithm for the (1,k)-FGC problem. (b) We present a 4-approximation algorithm for the (k,1)-FGC problem. For the unweighted FGC problem, where each edge has unit cost, we give a 16/11-approximation algorithm. This improves on the result of Adjiashvili et al. for this problem. The (p,q)-FGC model with p = 1 or q ≤ 1 can be cast as the Capacitated k-Connected Subgraph problem which is a special case of the well-known Capacitated Network Design problem. We denote the former problem by Cap-k-ECSS. An instance of this problem consists of an undirected graph G = (V,E), nonnegative integer edge-capacities {u_e}_{e ∈ E}, nonnegative edge-costs {c_e}_{e ∈ E}, and a positive integer k. The goal is to find a minimum-cost edge-set F ⊆ E such that every (non-trivial) cut of the capacitated subgraph H(V,F,u) has capacity at least k. We give a min(k, 2max_{e ∈ E} u_e)-approximation algorithm for this problem.
Cite as

Sylvia Boyd, Joseph Cheriyan, Arash Haddadan, and Sharat Ibrahimpur. Approximation Algorithms for Flexible Graph Connectivity. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{boyd_et_al:LIPIcs.FSTTCS.2021.9,
  author =	{Boyd, Sylvia and Cheriyan, Joseph and Haddadan, Arash and Ibrahimpur, Sharat},
  title =	{{Approximation Algorithms for Flexible Graph Connectivity}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.9},
  URN =		{urn:nbn:de:0030-drops-155206},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.9},
  annote =	{Keywords: Approximation Algorithms, Combinatorial Optimization, Network Design, Edge-Connectivity of Graphs, Reliability of Networks}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.81
Minimum-Norm Load Balancing Is (Almost) as Easy as Minimizing Makespan

Authors: Sharat Ibrahimpur and Chaitanya Swamy

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We consider the minimum-norm load-balancing (MinNormLB) problem, wherein there are n jobs, each of which needs to be assigned to one of m machines, and we are given the processing times {p_{ij}} of the jobs on the machines. We also have a monotone, symmetric norm f:ℝ^m → ℝ_{≥ 0}. We seek an assignment σ of jobs to machines that minimizes the f-norm of the induced load vector load->_σ ∈ ℝ_{≥ 0}^m, where load_σ(i) = ∑_{j:σ(j) = i}p_{ij}. This problem was introduced by [Deeparnab Chakrabarty and Chaitanya Swamy, 2019], and the current-best result for MinNormLB is a (4+ε)-approximation [Deeparnab Chakrabarty and Chaitanya Swamy, 2019]. In the stochastic version of MinNormLB, the job processing times are given by nonnegative random variables X_{ij}, and jobs are independent; the goal is to find an assignment σ that minimizes the expected f-norm of the induced random load vector. We obtain results that (essentially) match the best-known guarantees for deterministic makespan minimization (MinNormLB with 𝓁_∞ norm). For MinNormLB, we obtain a (2+ε)-approximation for unrelated machines, and a PTAS for identical machines. For stochastic MinNormLB, we consider the setting where the X_{ij}s are Poisson random variables, denoted PoisNormLB. Our main result here is a novel and powerful reduction showing that, for any machine environment (e.g., unrelated/identical machines), any α-approximation algorithm for MinNormLB in that machine environment yields a randomized α(1+ε)-approximation for PoisNormLB in that machine environment. Combining this with our results for MinNormLB, we immediately obtain a (2+ε)-approximation for PoisNormLB on unrelated machines, and a PTAS for PoisNormLB on identical machines. The latter result substantially generalizes a PTAS for makespan minimization with Poisson jobs obtained recently by [Anindya De et al., 2020].
Cite as

Sharat Ibrahimpur and Chaitanya Swamy. Minimum-Norm Load Balancing Is (Almost) as Easy as Minimizing Makespan. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ibrahimpur_et_al:LIPIcs.ICALP.2021.81,
  author =	{Ibrahimpur, Sharat and Swamy, Chaitanya},
  title =	{{Minimum-Norm Load Balancing Is (Almost) as Easy as Minimizing Makespan}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{81:1--81:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.81},
  URN =		{urn:nbn:de:0030-drops-141504},
  doi =		{10.4230/LIPIcs.ICALP.2021.81},
  annote =	{Keywords: Approximation algorithms, Load balancing, Minimum-norm optimization, LP rounding}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.61
A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Multisubgraph Problem in the Half-Integral Case

Authors: Sylvia Boyd, Joseph Cheriyan, Robert Cummings, Logan Grout, Sharat Ibrahimpur, Zoltán Szigeti, and Lu Wang

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

Abstract
Given a connected undirected graph G ̅ on n vertices, and non-negative edge costs c, the 2ECM problem is that of finding a 2-edge connected spanning multisubgraph of G ̅ of minimum cost. The natural linear program (LP) for 2ECM, which coincides with the subtour LP for the Traveling Salesman Problem on the metric closure of G ̅, gives a lower bound on the optimal cost. For instances where this LP is optimized by a half-integral solution x, Carr and Ravi (1998) showed that the integrality gap is at most 4/3: they show that the vector 4/3 x dominates a convex combination of incidence vectors of 2-edge connected spanning multisubgraphs of G ̅. We present a simpler proof of the result due to Carr and Ravi by applying an extension of Lovász’s splitting-off theorem. Our proof naturally leads to a 4/3-approximation algorithm for half-integral instances. Given a half-integral solution x to the LP for 2ECM, we give an O(n²)-time algorithm to obtain a 2-edge connected spanning multisubgraph of G ̅ whose cost is at most 4/3 c^T x.
Cite as

Sylvia Boyd, Joseph Cheriyan, Robert Cummings, Logan Grout, Sharat Ibrahimpur, Zoltán Szigeti, and Lu Wang. A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Multisubgraph Problem in the Half-Integral Case. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{boyd_et_al:LIPIcs.APPROX/RANDOM.2020.61,
  author =	{Boyd, Sylvia and Cheriyan, Joseph and Cummings, Robert and Grout, Logan and Ibrahimpur, Sharat and Szigeti, Zolt\'{a}n and Wang, Lu},
  title =	{{A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Multisubgraph Problem in the Half-Integral Case}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{61:1--61:12},
  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.2020.61},
  URN =		{urn:nbn:de:0030-drops-126643},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.61},
  annote =	{Keywords: 2-Edge Connectivity, Approximation Algorithms, Subtour LP for TSP}
}
  • Refine by Type
  • 13 Document/PDF
  • 6 Document/HTML

  • Refine by Publication Year
  • 6 2025
  • 3 2023
  • 1 2022
  • 2 2021
  • 1 2020

  • Refine by Author
  • 7 Ibrahimpur, Sharat
  • 3 Bansal, Ishan
  • 3 Cheriyan, Joseph
  • 3 Grout, Logan
  • 2 Boyd, Sylvia
  • Show More...

  • Refine by Series/Journal
  • 13 LIPIcs

  • Refine by Classification
  • 7 Theory of computation → Approximation algorithms analysis
  • 2 Mathematics of computing → Approximation algorithms
  • 2 Mathematics of computing → Combinatorial optimization
  • 2 Theory of computation → Caching and paging algorithms
  • 1 Mathematics of computing → Combinatorial algorithms
  • Show More...

  • Refine by Keyword
  • 6 Approximation Algorithms
  • 5 Approximation algorithms
  • 3 Network Design
  • 2 Caching
  • 2 Capacitated network design
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact