4 Search Results for "Koranteng, Ama"

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)

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@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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.32
Light Edge Fault Tolerant Graph Spanners

Authors: Greg Bodwin, Michael Dinitz, Ama Koranteng, and Lily Wang

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

Abstract
There has recently been significant interest in fault tolerant spanners, which are spanners that still maintain their stretch guarantees after some nodes or edges fail. This work has culminated in an almost complete understanding of the three-way tradeoff between stretch, sparsity, and number of faults tolerated. However, despite some progress in metric settings, there have been no results to date on the tradeoff in general graphs between stretch, lightness, and number of faults tolerated. We initiate the study of light edge fault tolerant (EFT) graph spanners, obtaining the first such results. First, we observe that lightness can be unbounded if we use the traditional definition (normalizing by the MST). We then argue that a natural definition of fault-tolerant lightness is to instead normalize by a min-weight fault tolerant connectivity preserver; essentially, a fault-tolerant version of the MST. However, even with this, we show that it is still not generally possible to construct f-EFT spanners whose weight compares reasonably to the weight of a min-weight f-EFT connectivity preserver. In light of this lower bound, it is natural to then consider bicriteria notions of lightness, where we compare the weight of an f-EFT spanner to a min-weight (f' > f)-EFT connectivity preserver. The most interesting question is to determine the minimum value of f' that allows for reasonable lightness upper bounds. Our main result is a precise answer to this question: f' = 2f. In particular, we show that the lightness can be untenably large (roughly n/k for a k-spanner) if one normalizes by the min-weight (2f-1)-EFT connectivity preserver. But if one normalizes by the min-weight 2f-EFT connectivity preserver, then we show that the lightness is bounded by just O(f^{1/2}) times the non-fault tolerant lightness (roughly n^{1/k} for a (1+ε)(2k-1)-spanner).
Cite as

Greg Bodwin, Michael Dinitz, Ama Koranteng, and Lily Wang. Light Edge Fault Tolerant Graph Spanners. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodwin_et_al:LIPIcs.ICALP.2025.32,
  author =	{Bodwin, Greg and Dinitz, Michael and Koranteng, Ama and Wang, Lily},
  title =	{{Light Edge Fault Tolerant Graph Spanners}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{32:1--32:20},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-234093},
  doi =		{10.4230/LIPIcs.ICALP.2025.32},
  annote =	{Keywords: Fault Tolerant Spanners, Light Spanners}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

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

Abstract
For a given graph G, a hopset H with hopbound β and stretch α is a set of edges such that between every pair of vertices u and v, there is a path with at most β hops in G ∪ H that approximates the distance between u and v up to a multiplicative stretch of α. Hopsets have found a wide range of applications for distance-based problems in various computational models since the 90s. More recently, there has been significant interest in understanding these fundamental objects from an existential and structural perspective. But all of this work takes a worst-case (or existential) point of view: How many edges do we need to add to satisfy a given hopbound and stretch requirement for any input graph? We initiate the study of the natural optimization variant of this problem: given a specific graph instance, what is the minimum number of edges that satisfy the hopbound and stretch requirements? We give approximation algorithms for a generalized hopset problem which, when combined with known existential bounds, lead to different approximation guarantees for various regimes depending on hopbound, stretch, and directed vs. undirected inputs. We complement our upper bounds with a lower bound that implies Label Cover hardness for directed hopsets and shortcut sets with hopbound at least 3.
Cite as

Michael Dinitz, Ama Koranteng, and Yasamin Nazari. Approximation Algorithms for Optimal Hopsets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.41
Relative Survivable Network Design

Authors: Michael Dinitz, Ama Koranteng, and Guy Kortsarz

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

Abstract
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum k-Edge-Connected Spanning Subgraph problem (k-ECSS), as well as nonuniform demands such as the Survivable Network Design problem. A weakness of these formulations, though, is that we are not able to ask for fault-tolerance larger than the connectivity. Taking inspiration from recent definitions and progress in graph spanners, we introduce and study new variants of these problems under a notion of relative fault-tolerance. Informally, we require not that two nodes are connected if there are a bounded number of faults (as in the classical setting), but that two nodes are connected if there are a bounded number of faults and the two nodes are connected in the underlying graph post-faults. That is, the subgraph we build must "behave" identically to the underlying graph with respect to connectivity after bounded faults. We define and introduce these problems, and provide the first approximation algorithms: a (1+4/k)-approximation for the unweighted relative version of k-ECSS, a 2-approximation for the weighted relative version of k-ECSS, and a 27/4-approximation for the special case of Relative Survivable Network Design with only a single demand with a connectivity requirement of 3. To obtain these results, we introduce a number of technical ideas that may of independent interest. First, we give a generalization of Jain’s iterative rounding analysis that works even when the cut-requirement function is not weakly supermodular, but instead satisfies a weaker definition we introduce and term local weak supermodularity. Second, we prove a structure theorem and design an approximation algorithm utilizing a new decomposition based on important separators, which are structures commonly used in fixed-parameter algorithms that have not commonly been used in approximation algorithms.
Cite as

Michael Dinitz, Ama Koranteng, and Guy Kortsarz. Relative Survivable Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dinitz_et_al:LIPIcs.APPROX/RANDOM.2022.41,
  author =	{Dinitz, Michael and Koranteng, Ama and Kortsarz, Guy},
  title =	{{Relative Survivable Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{41:1--41:19},
  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.2022.41},
  URN =		{urn:nbn:de:0030-drops-171632},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.41},
  annote =	{Keywords: Fault Tolerance, Network Design}
}
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