20 Search Results for "Abboud, Amir"

Document
DOI: 10.4230/LIPIcs.ITCS.2024.19
Spanning Adjacency Oracles in Sublinear Time

Authors: Greg Bodwin and Henry Fleischmann

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Suppose we are given an n-node, m-edge input graph G, and the goal is to compute a spanning subgraph H on O(n) edges. This can be achieved in linear O(m + n) time via breadth-first search. But can we hope for sublinear runtime in some range of parameters - for example, perhaps O(n^{1.9}) worst-case runtime, even when the input graph has n² edges? If the goal is to return H as an adjacency list, there are simple lower bounds showing that Ω(m + n) runtime is necessary. If the goal is to return H as an adjacency matrix, then we need Ω(n²) time just to write down the entries of the output matrix. However, we show that neither of these lower bounds still apply if instead the goal is to return H as an implicit adjacency matrix, which we call an adjacency oracle. An adjacency oracle is a data structure that gives a user the illusion that an adjacency matrix has been computed: it accepts edge queries (u, v), and it returns in near-constant time a bit indicating whether or not (u, v) ∈ E(H). Our main result is that, for any 0 < ε < 1, one can construct an adjacency oracle for a spanning subgraph on at most (1+ε)n edges, in Õ(n ε^{-1}) time (hence sublinear time on input graphs with m ≫ n edges), and that this construction time is near-optimal. Additional results include constructions of adjacency oracles for k-connectivity certificates and spanners, which are similarly sublinear on dense-enough input graphs. Our adjacency oracles are closely related to Local Computation Algorithms (LCAs) for graph sparsifiers; they can be viewed as LCAs with some computation moved to a preprocessing step, in order to speed up queries. Our oracles imply the first LCAs for computing sparse spanning subgraphs of general input graphs in Õ(n) query time, which works by constructing our adjacency oracle, querying it once, and then throwing the rest of the oracle away. This addresses an open problem of Rubinfeld [CSR '17].
Cite as

Greg Bodwin and Henry Fleischmann. Spanning Adjacency Oracles in Sublinear Time. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bodwin_et_al:LIPIcs.ITCS.2024.19,
  author =	{Bodwin, Greg and Fleischmann, Henry},
  title =	{{Spanning Adjacency Oracles in Sublinear Time}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.19},
  URN =		{urn:nbn:de:0030-drops-195475},
  doi =		{10.4230/LIPIcs.ITCS.2024.19},
  annote =	{Keywords: Graph algorithms, Sublinear algorithms, Data structures, Graph theory}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.25
Listing 4-Cycles

Authors: Amir Abboud, Seri Khoury, Oree Leibowitz, and Ron Safier

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
We study the fine-grained complexity of listing all 4-cycles in a graph on n nodes, m edges, and t such 4-cycles. The main result is an Õ(min(n²,m^{4/3})+t) upper bound, which is best-possible up to log factors unless the long-standing O(min(n²,m^{4/3})) upper bound for detecting a 4-cycle can be broken. Moreover, it almost-matches recent 3-SUM-based lower bounds for the problem by Abboud, Bringmann, and Fischer (STOC 2023) and independently by Jin and Xu (STOC 2023). Notably, our result separates 4-cycle listing from the closely related triangle listing for which higher conditional lower bounds exist, and rule out such a "detection plus t" bound. We also show by simple arguments that our bound cannot be extended to mild generalizations of the problem such as reporting all pairs of nodes that participate in a 4-cycle. [Independent work: Jin and Xu [Ce Jin and Yinzhan Xu, 2023] also present an algorithm with the same time bound.]
Cite as

Amir Abboud, Seri Khoury, Oree Leibowitz, and Ron Safier. Listing 4-Cycles. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.FSTTCS.2023.25,
  author =	{Abboud, Amir and Khoury, Seri and Leibowitz, Oree and Safier, Ron},
  title =	{{Listing 4-Cycles}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.25},
  URN =		{urn:nbn:de:0030-drops-193985},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.25},
  annote =	{Keywords: Graph algorithms, cycles listing, subgraph detection, fine-grained complexity}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.1
On Complexity of 1-Center in Various Metrics

Authors: Amir Abboud, MohammadHossein Bateni, Vincent Cohen-Addad, Karthik C. S., and Saeed Seddighin

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

Abstract
We consider the classic 1-center problem: Given a set P of n points in a metric space find the point in P that minimizes the maximum distance to the other points of P. We study the complexity of this problem in d-dimensional 𝓁_p-metrics and in edit and Ulam metrics over strings of length d. Our results for the 1-center problem may be classified based on d as follows. - Small d. Assuming the hitting set conjecture (HSC), we show that when d = ω(log n), no subquadratic algorithm can solve the 1-center problem in any of the 𝓁_p-metrics, or in the edit or Ulam metrics. - Large d. When d = Ω(n), we extend our conditional lower bound to rule out subquartic algorithms for the 1-center problem in edit metric (assuming Quantified SETH). On the other hand, we give a (1+ε)-approximation for 1-center in the Ulam metric with running time O_{ε}̃(nd+n²√d). We also strengthen some of the above lower bounds by allowing approximation algorithms or by reducing the dimension d, but only against a weaker class of algorithms which list all requisite solutions. Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of n strings each of length n, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.
Cite as

Amir Abboud, MohammadHossein Bateni, Vincent Cohen-Addad, Karthik C. S., and Saeed Seddighin. On Complexity of 1-Center in Various Metrics. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.APPROX/RANDOM.2023.1,
  author =	{Abboud, Amir and Bateni, MohammadHossein and Cohen-Addad, Vincent and Karthik C. S. and Seddighin, Saeed},
  title =	{{On Complexity of 1-Center in Various Metrics}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{1:1--1:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.1},
  URN =		{urn:nbn:de:0030-drops-188260},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.1},
  annote =	{Keywords: Center, Clustering, Edit metric, Ulam metric, Hamming metric, Fine-grained Complexity, Approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.2
On Diameter Approximation in Directed Graphs

Authors: Amir Abboud, Mina Dalirrooyfard, Ray Li, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs. approximation trade-off that is quite close to the upper bounds. In directed graphs, however, where only some of the upper bounds apply, much larger gaps remain. Since d(u,v) may not be the same as d(v,u), there are multiple ways to define the problem, the two most natural being the (one-way) diameter (max_(u,v) d(u,v)) and the roundtrip diameter (max_{u,v} d(u,v)+d(v,u)). In this paper we make progress on the outstanding open question for each of them. - We design the first algorithm for diameter in sparse directed graphs to achieve n^{1.5-ε} time with an approximation factor better than 2. The new upper bound trade-off makes the directed case appear more similar to the undirected case. Notably, this is the first algorithm for diameter in sparse graphs that benefits from fast matrix multiplication. - We design new hardness reductions separating roundtrip diameter from directed and undirected diameter. In particular, a 1.5-approximation in subquadratic time would refute the All-Nodes k-Cycle hypothesis, and any (2-ε)-approximation would imply a breakthrough algorithm for approximate 𝓁_∞-Closest-Pair. Notably, these are the first conditional lower bounds for diameter that are not based on SETH.
Cite as

Amir Abboud, Mina Dalirrooyfard, Ray Li, and Virginia Vassilevska Williams. On Diameter Approximation in Directed Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ESA.2023.2,
  author =	{Abboud, Amir and Dalirrooyfard, Mina and Li, Ray and Vassilevska Williams, Virginia},
  title =	{{On Diameter Approximation in Directed Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.2},
  URN =		{urn:nbn:de:0030-drops-186552},
  doi =		{10.4230/LIPIcs.ESA.2023.2},
  annote =	{Keywords: Diameter, Directed Graphs, Approximation Algorithms, Fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.3
Can You Solve Closest String Faster Than Exhaustive Search?

Authors: Amir Abboud, Nick Fischer, Elazar Goldenberg, Karthik C. S., and Ron Safier

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set X ⊆ Σ^d of n strings, find the string x^* minimizing the radius of the smallest Hamming ball around x^* that encloses all the strings in X. In this paper, we investigate whether the Closest String problem admits algorithms that are faster than the trivial exhaustive search algorithm. We obtain the following results for the two natural versions of the problem: - In the continuous Closest String problem, the goal is to find the solution string x^* anywhere in Σ^d. For binary strings, the exhaustive search algorithm runs in time O(2^d poly(nd)) and we prove that it cannot be improved to time O(2^{(1-ε) d} poly(nd)), for any ε > 0, unless the Strong Exponential Time Hypothesis fails. - In the discrete Closest String problem, x^* is required to be in the input set X. While this problem is clearly in polynomial time, its fine-grained complexity has been pinpointed to be quadratic time n^{2 ± o(1)} whenever the dimension is ω(log n) < d < n^o(1). We complement this known hardness result with new algorithms, proving essentially that whenever d falls out of this hard range, the discrete Closest String problem can be solved faster than exhaustive search. In the small-d regime, our algorithm is based on a novel application of the inclusion-exclusion principle. Interestingly, all of our results apply (and some are even stronger) to the natural dual of the Closest String problem, called the Remotest String problem, where the task is to find a string maximizing the Hamming distance to all the strings in X.
Cite as

Amir Abboud, Nick Fischer, Elazar Goldenberg, Karthik C. S., and Ron Safier. Can You Solve Closest String Faster Than Exhaustive Search?. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ESA.2023.3,
  author =	{Abboud, Amir and Fischer, Nick and Goldenberg, Elazar and Karthik C. S. and Safier, Ron},
  title =	{{Can You Solve Closest String Faster Than Exhaustive Search?}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.3},
  URN =		{urn:nbn:de:0030-drops-186566},
  doi =		{10.4230/LIPIcs.ESA.2023.3},
  annote =	{Keywords: Closest string, fine-grained complexity, SETH, inclusion-exclusion}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.4
What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?

Authors: Amir Abboud, Shay Mozes, and Oren Weimann

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The Voronoi diagrams technique, introduced by Cabello [SODA'17] to compute the diameter of planar graphs in subquadratic time, has revolutionized the field of distance computations in planar graphs. We present novel applications of this technique in static, fault-tolerant, and partially-dynamic undirected unweighted planar graphs, as well as some new limitations. - In the static case, we give n^{3+o(1)}/D² and Õ(n⋅D²) time algorithms for computing the diameter of a planar graph G with diameter D. These are faster than the state of the art Õ(n^{5/3}) [SODA'18] when D < n^{1/3} or D > n^{2/3}. - In the fault-tolerant setting, we give an n^{7/3+o(1)} time algorithm for computing the diameter of G⧵ {e} for every edge e in G (the replacement diameter problem). This should be compared with the naive Õ(n^{8/3}) time algorithm that runs the static algorithm for every edge. - In the incremental setting, where we wish to maintain the diameter while adding edges, we present an algorithm with total running time n^{7/3+o(1)}. This should be compared with the naive Õ(n^{8/3}) time algorithm that runs the static algorithm after every update. - We give a lower bound (conditioned on the SETH) ruling out an amortized O(n^{1-ε}) update time for maintaining the diameter in weighted planar graph. The lower bound holds even for incremental or decremental updates. Our upper bounds are obtained by novel uses and manipulations of Voronoi diagrams. These include maintaining the Voronoi diagram when edges of the graph are deleted, allowing the sites of the Voronoi diagram to lie on a BFS tree level (rather than on boundaries of r-division), and a new reduction from incremental diameter to incremental distance oracles that could be of interest beyond planar graphs. Our lower bound is the first lower bound for a dynamic planar graph problem that is conditioned on the SETH.
Cite as

Amir Abboud, Shay Mozes, and Oren Weimann. What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ESA.2023.4,
  author =	{Abboud, Amir and Mozes, Shay and Weimann, Oren},
  title =	{{What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.4},
  URN =		{urn:nbn:de:0030-drops-186575},
  doi =		{10.4230/LIPIcs.ESA.2023.4},
  annote =	{Keywords: Planar graphs, diameter, dynamic graphs, fault tolerance}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.1
Worst-Case to Expander-Case Reductions

Authors: Amir Abboud and Nathan Wallheimer

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems are as easy on worst-case graphs as they are on expanders, and (2) suspect that expander decompositions are the key to breaking the remaining longstanding barriers in fine-grained complexity. We set out to investigate the extent to which these two things are true (and for which problems). Towards this end, we put forth the concept of worst-case to expander-case self-reductions. We design a collection of such reductions for fundamental graph problems, verifying belief (1) for them. The list includes k-Clique, 4-Cycle, Maximum Cardinality Matching, Vertex-Cover, and Minimum Dominating Set. Interestingly, for most (but not all) of these problems the proof is via a simple gadget reduction, not via expander decompositions, showing that this hammer is effectively useless against the problem and contradicting (2).
Cite as

Amir Abboud and Nathan Wallheimer. Worst-Case to Expander-Case Reductions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ITCS.2023.1,
  author =	{Abboud, Amir and Wallheimer, Nathan},
  title =	{{Worst-Case to Expander-Case Reductions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.1},
  URN =		{urn:nbn:de:0030-drops-175044},
  doi =		{10.4230/LIPIcs.ITCS.2023.1},
  annote =	{Keywords: Fine-Grained Complexity, Expander Decomposition, Reductions, Exact and Parameterized Complexity, Expander Graphs, Triangle, Maximum Matching, Clique, 4-Cycle, Vertex Cover, Dominating Set}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.7
Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems

Authors: Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. 1) We give a polynomial-time approximation scheme (PTAS) for a diversified search ranking problem [Nikhil Bansal et al., 2010] whose objective is to minimizes the discounted cumulative gain. Our PTAS runs in time n^{2^O(log(1/ε)/ε)} ⋅ m^O(1) where n denotes the number of elements in the databases and m denotes the number of constraints. Complementing this result, we show that no PTAS can run in time f(ε) ⋅ (nm)^{2^o(1/ε)} assuming Gap-ETH and therefore our running time is nearly tight. Both our upper and lower bounds answer open questions from [Nikhil Bansal et al., 2010]. 2) We next consider the Max-Sum Dispersion problem, whose objective is to select k out of n elements from a database that maximizes the dispersion, which is defined as the sum of the pairwise distances under a given metric. We give a quasipolynomial-time approximation scheme (QPTAS) for the problem which runs in time n^{O_ε(log n)}. This improves upon previously known polynomial-time algorithms with approximate ratios 0.5 [Refael Hassin et al., 1997; Allan Borodin et al., 2017]. Furthermore, we observe that reductions from previous work rule out approximation schemes that run in n^õ_ε(log n) time assuming ETH. 3) Finally, we consider a generalization of Max-Sum Dispersion called Max-Sum Diversification. In addition to the sum of pairwise distance, the objective also includes another function f. For monotone submodular function f, we give a quasipolynomial-time algorithm with approximation ratio arbitrarily close to (1-1/e). This improves upon the best polynomial-time algorithm which has approximation ratio 0.5 [Allan Borodin et al., 2017]. Furthermore, the (1-1/e) factor is also tight as achieving better-than-(1-1/e) approximation is NP-hard [Uriel Feige, 1998].
Cite as

Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi. Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ICALP.2022.7,
  author =	{Abboud, Amir and Cohen-Addad, Vincent and Lee, Euiwoong and Manurangsi, Pasin},
  title =	{{Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.7},
  URN =		{urn:nbn:de:0030-drops-163481},
  doi =		{10.4230/LIPIcs.ICALP.2022.7},
  annote =	{Keywords: Approximation Algorithms, Complexity, Data Mining, Diversification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.109
Faster Cut-Equivalent Trees in Simple Graphs

Authors: Tianyi Zhang

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Let G = (V, E) be an undirected connected simple graph on n vertices. A cut-equivalent tree of G is an edge-weighted tree on the same vertex set V, such that for any pair of vertices s, t ∈ V, the minimum (s, t)-cut in the tree is also a minimum (s, t)-cut in G, and these two cuts have the same cut value. In a recent paper [Abboud, Krauthgamer and Trabelsi, STOC 2021], the authors propose the first subcubic time algorithm for constructing a cut-equivalent tree. More specifically, their algorithm has Õ(n^{2.5}) running time. Later on, this running time was significantly improved to n^{2+o(1)} by two independent works [Abboud, Krauthgamer and Trabelsi, FOCS 2021] and [Li, Panigrahi, Saranurak, FOCS 2021], and then to (m+n^{1.9})^{1+o(1)} by [Abboud, Krauthgamer and Trabelsi, SODA 2022]. In this paper, we improve the running time to Õ(n²) graphs if near-linear time max-flow algorithms exist, or Õ(n^{17/8}) using the currently fastest max-flow algorithm. Although our algorithm is slower than previous works, the runtime bound becomes better by a sub-polynomial factor in dense simple graphs when assuming near-linear time max-flow algorithms.
Cite as

Tianyi Zhang. Faster Cut-Equivalent Trees in Simple Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 109:1-109:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{zhang:LIPIcs.ICALP.2022.109,
  author =	{Zhang, Tianyi},
  title =	{{Faster Cut-Equivalent Trees in Simple Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{109:1--109:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.109},
  URN =		{urn:nbn:de:0030-drops-164507},
  doi =		{10.4230/LIPIcs.ICALP.2022.109},
  annote =	{Keywords: graph algorithms, minimum cuts, max-flow}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.115
3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time

Authors: Masoud Seddighin and Saeed Seddighin

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Tree edit distance is a well-known generalization of the edit distance problem to rooted trees. In this problem, the goal is to transform a rooted tree into another rooted tree via (i) node addition, (ii) node deletion, and (iii) node relabel. In this work, we give a truly subquadratic time algorithm that approximates tree edit distance within a factor 3+ε. Our result is obtained through a novel extension of a 3-step framework that approximates edit distance in truly subquadratic time. This framework has also been previously used to approximate longest common subsequence in subquadratic time.
Cite as

Masoud Seddighin and Saeed Seddighin. 3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 115:1-115:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{seddighin_et_al:LIPIcs.ITCS.2022.115,
  author =	{Seddighin, Masoud and Seddighin, Saeed},
  title =	{{3+\epsilon Approximation of Tree Edit Distance in Truly Subquadratic Time}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{115:1--115:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.115},
  URN =		{urn:nbn:de:0030-drops-157116},
  doi =		{10.4230/LIPIcs.ITCS.2022.115},
  annote =	{Keywords: tree edit distance, approximation, subquadratic, edit distance}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.7
Fine-Grained Hardness for Edit Distance to a Fixed Sequence

Authors: Amir Abboud and Virginia Vassilevska Williams

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

Abstract
Nearly all quadratic lower bounds conditioned on the Strong Exponential Time Hypothesis (SETH) start by reducing k-SAT to the Orthogonal Vectors (OV) problem: Given two sets A,B of n binary vectors, decide if there is an orthogonal pair a ∈ A, b ∈ B. In this paper, we give an alternative reduction in which the set A does not depend on the input to k-SAT; thus, the quadratic lower bound for OV holds even if one of the sets is fixed in advance. Using the reductions in the literature from OV to other problems such as computing similarity measures on strings, we get hardness results of a stronger kind: there is a family of sequences {S_n}_{n = 1}^{∞}, |S_n| = n such that computing the Edit Distance between an input sequence X of length n and the (fixed) sequence S_n requires n^{2-o(1)} time under SETH.
Cite as

Amir Abboud and Virginia Vassilevska Williams. Fine-Grained Hardness for Edit Distance to a Fixed Sequence. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ICALP.2021.7,
  author =	{Abboud, Amir and Vassilevska Williams, Virginia},
  title =	{{Fine-Grained Hardness for Edit Distance to a Fixed Sequence}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{7:1--7:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.7},
  URN =		{urn:nbn:de:0030-drops-140768},
  doi =		{10.4230/LIPIcs.ICALP.2021.7},
  annote =	{Keywords: SAT, edit distance, fine-grained complexity, conditional lower bound, sequence alignment}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.4
Scheduling Lower Bounds via AND Subset Sum

Authors: Amir Abboud, Karl Bringmann, Danny Hermelin, and Dvir Shabtay

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Given N instances (X_1,t_1),…,(X_N,t_N) of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers X_i has a subset that sums up to the target integer t_i. We prove that this problem cannot be solved in time Õ((N ⋅ t_max)^{1-ε}), for t_max = max_i t_i and any ε > 0, assuming the ∀ ∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude Õ(n+P_max⋅n^{1-ε})-time algorithms for several scheduling problems on n jobs with maximum processing time P_max, assuming ∀∃-SETH. These include classical problems such as 1||∑ w_jU_j, the problem of minimizing the total weight of tardy jobs on a single machine, and P₂||∑ U_j, the problem of minimizing the number of tardy jobs on two identical parallel machines.
Cite as

Amir Abboud, Karl Bringmann, Danny Hermelin, and Dvir Shabtay. Scheduling Lower Bounds via AND Subset Sum. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ICALP.2020.4,
  author =	{Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir},
  title =	{{Scheduling Lower Bounds via AND Subset Sum}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.4},
  URN =		{urn:nbn:de:0030-drops-124119},
  doi =		{10.4230/LIPIcs.ICALP.2020.4},
  annote =	{Keywords: SETH, fine grained complexity, Subset Sum, scheduling}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.5
On the Fine-Grained Complexity of Parity Problems

Authors: Amir Abboud, Shon Feller, and Oren Weimann

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We consider the parity variants of basic problems studied in fine-grained complexity. We show that finding the exact solution is just as hard as finding its parity (i.e. if the solution is even or odd) for a large number of classical problems, including All-Pairs Shortest Paths (APSP), Diameter, Radius, Median, Second Shortest Path, Maximum Consecutive Subsums, Min-Plus Convolution, and 0/1-Knapsack. A direct reduction from a problem to its parity version is often difficult to design. Instead, we revisit the existing hardness reductions and tailor them in a problem-specific way to the parity version. Nearly all reductions from APSP in the literature proceed via the (subcubic-equivalent but simpler) Negative Weight Triangle (NWT) problem. Our new modified reductions also start from NWT or a non-standard parity variant of it. We are not able to establish a subcubic-equivalence with the more natural parity counting variant of NWT, where we ask if the number of negative triangles is even or odd. Perhaps surprisingly, we justify this by designing a reduction from the seemingly-harder Zero Weight Triangle problem, showing that parity is (conditionally) strictly harder than decision for NWT.
Cite as

Amir Abboud, Shon Feller, and Oren Weimann. On the Fine-Grained Complexity of Parity Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{abboud_et_al:LIPIcs.ICALP.2020.5,
  author =	{Abboud, Amir and Feller, Shon and Weimann, Oren},
  title =	{{On the Fine-Grained Complexity of Parity Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.5},
  URN =		{urn:nbn:de:0030-drops-124127},
  doi =		{10.4230/LIPIcs.ICALP.2020.5},
  annote =	{Keywords: All-pairs shortest paths, Fine-grained complexity, Diameter, Distance product, Min-plus convolution, Parity problems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.1
Hardness Amplification of Optimization Problems

Authors: Elazar Goldenberg and Karthik C. S.

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem Π is direct product feasible if it is possible to efficiently aggregate any k instances of Π and form one large instance of Π such that given an optimal feasible solution to the larger instance, we can efficiently find optimal feasible solutions to all the k smaller instances. Given a direct product feasible optimization problem Π, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of Π of size n such that every randomized algorithm running in time t(n) fails to solve Π on 1/α(n) fraction of inputs sampled from D, then, assuming some relationships on α(n) and t(n), there is a distribution D' over instances of Π of size O(n⋅α(n)) such that every randomized algorithm running in time t(n)/poly(α(n)) fails to solve Π on 99/100 fraction of inputs sampled from D'. As a consequence of the above theorem, we show hardness amplification of problems in various classes such as NP-hard problems like Max-Clique, Knapsack, and Max-SAT, problems in P such as Longest Common Subsequence, Edit Distance, Matrix Multiplication, and even problems in TFNP such as Factoring and computing Nash equilibrium.
Cite as

Elazar Goldenberg and Karthik C. S.. Hardness Amplification of Optimization Problems. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{goldenberg_et_al:LIPIcs.ITCS.2020.1,
  author =	{Goldenberg, Elazar and Karthik C. S.},
  title =	{{Hardness Amplification of Optimization Problems}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.1},
  URN =		{urn:nbn:de:0030-drops-116863},
  doi =		{10.4230/LIPIcs.ITCS.2020.1},
  annote =	{Keywords: hardness amplification, average case complexity, direct product, optimization problems, fine-grained complexity, TFNP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.53
Monochromatic Triangles, Intermediate Matrix Products, and Convolutions

Authors: Andrea Lincoln, Adam Polak, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(n^ω) time algorithms for ω < 2.373. On the other hand, the (min,+) matrix product which is at the heart of many fundamental graph problems such as All-Pairs Shortest Paths, has received only minor n^o(1) improvements over its brute-force cubic running time and is widely conjectured to require n^{3-o(1)} time. There is a plethora of matrix products and graph problems whose complexity seems to lie in the middle of these two problems. For instance, the Min-Max matrix product, the Minimum Witness matrix product, All-Pairs Shortest Paths in directed unweighted graphs and determining whether an edge-colored graph contains a monochromatic triangle, can all be solved in Õ(n^{(3+ω)/2}) time. While slight improvements are sometimes possible using rectangular matrix multiplication, if ω=2, the best runtimes for these "intermediate" problems are all Õ(n^2.5). A similar phenomenon occurs for convolution problems. Here, using the FFT, the usual (+,×)-convolution of two n-length sequences can be solved in O(n log n) time, while the (min,+) convolution is conjectured to require n^{2-o(1)} time, the brute force running time for convolution problems. There are analogous intermediate problems that can be solved in O(n^1.5) time, but seemingly not much faster: Min-Max convolution, Minimum Witness convolution, etc. Can one improve upon the running times for these intermediate problems, in either the matrix product or the convolution world? Or, alternatively, can one relate these problems to each other and to other key problems in a meaningful way? This paper makes progress on these questions by providing a network of fine-grained reductions. We show for instance that APSP in directed unweighted graphs and Minimum Witness product can be reduced to both the Min-Max product and a variant of the monochromatic triangle problem, so that a significant improvement over n^{(3+ω)/2} time for any of the latter problems would result in a similar improvement for both of the former problems. We also show that a natural convolution variant of monochromatic triangle is fine-grained equivalent to the famous 3SUM problem. As this variant is solvable in O(n^1.5) time and 3SUM is in O(n^2) time (and is conjectured to require n^{2-o(1)} time), our result gives the first fine-grained equivalence between natural problems of different running times. We also relate 3SUM to monochromatic triangle, and a coin change problem to monochromatic convolution, and thus to 3SUM.
Cite as

Andrea Lincoln, Adam Polak, and Virginia Vassilevska Williams. Monochromatic Triangles, Intermediate Matrix Products, and Convolutions. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 53:1-53:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{lincoln_et_al:LIPIcs.ITCS.2020.53,
  author =	{Lincoln, Andrea and Polak, Adam and Vassilevska Williams, Virginia},
  title =	{{Monochromatic Triangles, Intermediate Matrix Products, and Convolutions}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{53:1--53:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.53},
  URN =		{urn:nbn:de:0030-drops-117382},
  doi =		{10.4230/LIPIcs.ITCS.2020.53},
  annote =	{Keywords: 3SUM, fine-grained complexity, matrix multiplication, monochromatic triangle}
}
  • Refine by Author
  • 15 Abboud, Amir
  • 3 Karthik C. S.
  • 3 Vassilevska Williams, Virginia
  • 2 Bringmann, Karl
  • 2 Cohen-Addad, Vincent
  • Show More...

  • Refine by Classification
  • 7 Theory of computation → Problems, reductions and completeness
  • 6 Theory of computation → Design and analysis of algorithms
  • 3 Theory of computation → Graph algorithms analysis
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Computational complexity and cryptography
  • Show More...

  • Refine by Keyword
  • 6 fine-grained complexity
  • 3 Fine-Grained Complexity
  • 2 Approximation Algorithms
  • 2 Diameter
  • 2 Fine-grained Complexity
  • Show More...

  • Refine by Type
  • 20 document

  • Refine by Publication Year
  • 6 2023
  • 4 2020
  • 3 2022
  • 2 2018
  • 2 2019
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact