16 Search Results for "Derakhshan, Mahsa"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.51
Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems

Authors: Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu

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

Abstract
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing notions of sparsification measure the level of sparsity, called degree, as the ratio of queried items to the optimal solution size. While effective for matching and matroid-type problems with uniform structures, this cardinality-based approach fails for knapsack-type constraints where feasible sets exhibit dramatic structural variation. We introduce a polyhedral sparsification framework that measures the degree as the smallest scalar needed to embed the query set within a scaled feasibility polytope, naturally capturing redundancy without relying on cardinality. Our main contribution establishes that knapsack, multiple knapsack, and generalized assignment problems admit (1-ε)-approximate sparsifiers with degree polynomial in 1/p and 1/ε - where p denotes the independent activation probability of each element - remarkably independent of problem dimensions. The key insight involves grouping items with similar weights and deploying a charging argument: when our query set misses an optimal item, we either substitute it directly with a queried item from the same group or leverage that group’s excess contribution to compensate for the loss. This reveals an intriguing complexity-theoretic separation - while the multiple knapsack problem lacks an FPTAS and generalized assignment is APX-hard, their sparsification counterparts admit efficient (1-ε)-approximation algorithms that identify polynomial degree query sets. Finally, we raise an open question: can such sparsification extend to general integer linear programs with degree independent of problem dimensions?
Cite as

Shaddin Dughmi, Yusuf Hakan Kalayci, and Xinyu Liu. Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 51:1-51:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{dughmi_et_al:LIPIcs.ITCS.2026.51,
  author =	{Dughmi, Shaddin and Kalayci, Yusuf Hakan and Liu, Xinyu},
  title =	{{Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{51:1--51:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.51},
  URN =		{urn:nbn:de:0030-drops-253386},
  doi =		{10.4230/LIPIcs.ITCS.2026.51},
  annote =	{Keywords: Packing Problems, Assignment Problems, Stochastic Selection, Sparsification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.75
Prior-Independent and Subgame Optimal Online Algorithms

Authors: Jason Hartline, Aleck Johnsen, and Anant Shah

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

Abstract
This paper develops two game-theoretic notions of beyond worst-case analysis that give better than worst-case guarantees on natural inputs. We illustrate them through the finite-horizon ski-rental problem. First, we consider prior-independent design and analysis of online algorithms where, rather than choosing a worst-case input, the adversary chooses a worst-case independent and identical distribution over inputs. Prior-independent online algorithms are generally analytically intractable; instead we give a fully polynomial-time approximation scheme to compute them. Second, we consider the worst-case design of algorithms. We define "subgame optimality" which is stronger than worst-case optimality in that it requires the algorithm to take advantage of an adversary not playing a worst-case input. Algorithms that focus only on the worst case can be far from subgame optimal. Highlighting the potential improvement from these paradigms for the finite-horizon ski-rental problem, we empirically compare worst-case, subgame optimal, and prior-independent algorithms in the prior-independent framework. Finally, we analyze the structure of their decisions across input sequences: the prior-independent algorithm exhibits more extreme adaptations to observed data, in contrast with the more conservative behavior of worst-case and subgame optimal algorithms.
Cite as

Jason Hartline, Aleck Johnsen, and Anant Shah. Prior-Independent and Subgame Optimal Online Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{hartline_et_al:LIPIcs.ITCS.2026.75,
  author =	{Hartline, Jason and Johnsen, Aleck and Shah, Anant},
  title =	{{Prior-Independent and Subgame Optimal Online Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{75:1--75:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.75},
  URN =		{urn:nbn:de:0030-drops-253622},
  doi =		{10.4230/LIPIcs.ITCS.2026.75},
  annote =	{Keywords: online algorithms, prior-independent algorithm design, zero-sum games}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.67
Query Lower Bounds for Correlation Clustering Under Memory Constraints

Authors: Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou

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

Abstract
This work initiates the study of memory–query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non‑edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of ε n², any algorithm requires Ω(n/ε²) adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make ≫ n/ε² adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.
Cite as

Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou. Query Lower Bounds for Correlation Clustering Under Memory Constraints. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.ITCS.2026.67,
  author =	{Garg, Sumegha and He, Songhua and Papakonstantinou, Periklis A.},
  title =	{{Query Lower Bounds for Correlation Clustering Under Memory Constraints}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{67:1--67:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.67},
  URN =		{urn:nbn:de:0030-drops-253542},
  doi =		{10.4230/LIPIcs.ITCS.2026.67},
  annote =	{Keywords: correlation clustering, query-space complexity, information theory}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.6
On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms

Authors: Jens Schlöter

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

Abstract
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the corresponding profits. The actual item profit can be obtained via a query. The goal of the problem is to adaptively query item profits until the revealed information suffices to compute an optimal (or approximate) solution to the underlying knapsack instance. Since queries are costly, the objective is to minimize the number of queries. In the offline variant of this problem, we assume knowledge of the precise profits and the task is to compute a query set of minimum cardinality that a third party without access to the profits could use to identify an optimal (or approximate) knapsack solution. We show that this offline variant is complete for the second-level of the polynomial hierarchy, i.e., Σ₂^p-complete, and cannot be approximated within a non-trivial factor unless Σ₂^p = Δ₂^p. Motivated by these strong hardness results, we consider a "resource-augmented" variant of the problem where the requirements on the query set computed by an algorithm are less strict than the requirements on the optimal solution we compare against. More precisely, a query set computed by the algorithm must reveal sufficient information to identify an approximate knapsack solution, while the optimal query set we compare against has to reveal sufficient information to identify an optimal solution. We show that this resource-augmented setting allows interesting non-trivial algorithmic results.
Cite as

Jens Schlöter. On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{schloter:LIPIcs.ESA.2025.6,
  author =	{Schl\"{o}ter, Jens},
  title =	{{On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{6:1--6:15},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-244740},
  doi =		{10.4230/LIPIcs.ESA.2025.6},
  annote =	{Keywords: Explorable uncertainty, knapsack, queries, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.48
Improved Streaming Edge Coloring

Authors: Shiri Chechik, Hongyi Chen, and Tianyi Zhang

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

Abstract
Given a graph, an edge coloring assigns colors to edges so that no pairs of adjacent edges share the same color. We are interested in edge coloring algorithms under the W-streaming model. In this model, the algorithm does not have enough memory to hold the entire graph, so the edges of the input graph are read from a data stream one by one in an unknown order, and the algorithm needs to print a valid edge coloring in an output stream. The performance of the algorithm is measured by the amount of space and the number of different colors it uses. This streaming edge coloring problem has been studied by several works in recent years. When the input graph contains n vertices and has maximum vertex degree Δ, it is known that in the W-streaming model, an O(Δ²)-edge coloring can be computed deterministically with Õ(n) space [Ansari, Saneian, and Zarrabi-Zadeh, 2022], or an O(Δ^{1.5})-edge coloring can be computed by a Õ(n)-space randomized algorithm [Behnezhad, Saneian, 2024] [Chechik, Mukhtar, Zhang, 2024]. In this paper, we achieve polynomial improvement over previous results. Specifically, we show how to improve the number of colors to Õ(Δ^{4/3+ε}) using space Õ(n) deterministically, for any constant ε > 0. This is the first deterministic result that bypasses the quadratic bound on the number of colors while using near-linear space.
Cite as

Shiri Chechik, Hongyi Chen, and Tianyi Zhang. Improved Streaming Edge Coloring. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chechik_et_al:LIPIcs.ICALP.2025.48,
  author =	{Chechik, Shiri and Chen, Hongyi and Zhang, Tianyi},
  title =	{{Improved Streaming Edge Coloring}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{48:1--48:18},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-234257},
  doi =		{10.4230/LIPIcs.ICALP.2025.48},
  annote =	{Keywords: edge coloring, streaming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.77
Minimizing Recourse in an Adaptive Balls and Bins Game

Authors: Adi Fine, Haim Kaplan, and Uri Stemmer

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

Abstract
We consider a simple load-balancing game between an algorithm and an adaptive adversary. In a simplified version of this game, the adversary observes the assignment of jobs to machines and selects a machine to kill. The algorithm must then restart the jobs from the failed machine on other machines. The adversary repeats this process, observing the new assignment and eliminating another machine, and so on. The adversary aims to force the algorithm to perform many restarts, while we seek a robust algorithm that minimizes restarts regardless of the adversary’s strategy. This game was recently introduced by Bhattacharya et al. for designing a 3-spanner with low recourse against an adaptive adversary. We prove that a simple algorithm, which assigns each job to a randomly chosen live bin, incurs O(n log n) recourse against an adaptive adversary. This enables us to construct a much simpler 3-spanner with a recourse that is smaller by a factor of O(log² n) compared to the previous construction, without increasing the update time or the size of the spanner. This motivates a careful examination of the range of attacks an adaptive adversary can deploy against simple algorithms before resorting to more complex ones. As our case study demonstrates, this attack space may not be as large as it initially appears, enabling the development of robust algorithms that are both simpler and easier to analyze.
Cite as

Adi Fine, Haim Kaplan, and Uri Stemmer. Minimizing Recourse in an Adaptive Balls and Bins Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 77:1-77:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fine_et_al:LIPIcs.ICALP.2025.77,
  author =	{Fine, Adi and Kaplan, Haim and Stemmer, Uri},
  title =	{{Minimizing Recourse in an Adaptive Balls and Bins Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{77:1--77:19},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-234544},
  doi =		{10.4230/LIPIcs.ICALP.2025.77},
  annote =	{Keywords: Adaptive adversary, load-balancing game, balls-and-bins, randomized algorithms, dynamic 3-spanner, dynamic graph algorithms, adversarial robustness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.58
A New Impossibility Result for Online Bipartite Matching Problems

Authors: Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani

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

Abstract
Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi [Manshadi et al., 2011] in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio. In this paper we show that no algorithm can achieve a competitive ratio better than 1- e/(e^e) = 0.82062…, improving upon the 0.823 upper bound presented in [Manshadi et al., 2011]. Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1 - 1/e, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.
Cite as

Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani. A New Impossibility Result for Online Bipartite Matching Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chierichetti_et_al:LIPIcs.ICALP.2025.58,
  author =	{Chierichetti, Flavio and Giacchini, Mirko and Panconesi, Alessandro and Vattani, Andrea},
  title =	{{A New Impossibility Result for Online Bipartite Matching Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{58:1--58:20},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-234354},
  doi =		{10.4230/LIPIcs.ICALP.2025.58},
  annote =	{Keywords: Bipartite Matching, Random Graphs, Competitive Ratio}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.42
Fitting Tree Metrics and Ultrametrics in Data Streams

Authors: Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis

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

Abstract
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Formally, given a positive distance function D: binom(V,2) → ℝ_{>0}, the goal is to find a tree (or an ultrametric) T including all elements of set V, such that the difference between the distances among vertices in T and those specified by D is minimized. Numerical taxonomy was first introduced by Sneath and Sokal [Nature 1962], and since then it has been studied extensively in both biology and computer science. In this paper, we initiate the study of ultrametric and tree metric fitting problems in the semi-streaming model, where the distances between pairs of elements from V (with |V| = n), defined by the function D, can arrive in an arbitrary order. We study these problems under various distance norms; namely the 𝓁₀ objective, which aims to minimize the number of modified entries in D to fit a tree-metric or an ultrametric; the 𝓁₁ objective, which seeks to minimize the total sum of distance errors across all pairs of points in V; and the 𝓁_∞ objective, which focuses on minimizing the maximum error incurred by any entries in D. - Our first result addresses the 𝓁₀ objective. We provide a single-pass polynomial-time Õ(n)-space O(1) approximation algorithm for ultrametrics and prove that no single-pass exact algorithm exists, even with exponential time. - Next, we show that the algorithm for 𝓁₀ implies an O(Δ/δ) approximation for the 𝓁₁ objective, where Δ is the maximum, and δ is the minimum absolute difference between distances in the input. This bound matches the best-known approximation for the RAM model using a combinatorial algorithm when Δ/δ = O(n). - For the 𝓁_∞ objective, we provide a complete characterization of the ultrametric fitting problem. First, we present a single-pass polynomial-time Õ(n)-space 2-approximation algorithm and show that no better than 2-approximation is possible, even with exponential time. Furthermore, we show that with an additional pass, it is possible to achieve a polynomial-time exact algorithm for ultrametrics. - Finally, we extend all these results to tree metrics by using only one additional pass through the stream and without asymptotically increasing the approximation factor.
Cite as

Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis. Fitting Tree Metrics and Ultrametrics in Data Streams. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{carmel_et_al:LIPIcs.ICALP.2025.42,
  author =	{Carmel, Amir and Das, Debarati and Kipouridis, Evangelos and Pipis, Evangelos},
  title =	{{Fitting Tree Metrics and Ultrametrics in Data Streams}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{42:1--42:21},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-234197},
  doi =		{10.4230/LIPIcs.ICALP.2025.42},
  annote =	{Keywords: Streaming, Clustering, Ultrametrics, Tree metrics, Distance fitting}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.66
One-Way Communication Complexity of Minimum Vertex Cover in General Graphs

Authors: Mahsa Derakhshan, Andisheh Ghasemi, and Rajmohan Rajaraman

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

Abstract
We study the communication complexity of the Minimum Vertex Cover (MVC) problem on general graphs within the k-party one-way communication model. Edges of an arbitrary n-vertex graph are distributed among k parties. The objective is for the parties to collectively find a small vertex cover of the graph while adhering to a communication protocol where each party sequentially sends a message to the next until the last party outputs a valid vertex cover of the whole graph. We are particularly interested in the trade-off between the size of the messages sent and the approximation ratio of the output solution. It is straightforward to see that any constant approximation protocol for MVC requires communicating Ω(n) bits. Additionally, there exists a trivial 2-approximation protocol where the parties collectively find a maximal matching of the graph greedily and return the subset of vertices matched. This raises a natural question: What is the best approximation ratio achievable using optimal communication of O(n)? We design a protocol with an approximation ratio of (2-2^{-k+1}+ε) and O(n) communication for any desirably small constant ε > 0, which is strictly better than 2 for any constant number of parties. Moreover, we show that achieving an approximation ratio smaller than 3/2 for the two-party case requires n^{1 + Ω(1/lg lg n)} communication, thereby establishing the tightness of our protocol for two parties. A notable aspect of our protocol is that no edges are communicated between the parties. Instead, for any 1 ≤ i < k, the i-th party only communicates a constant number of vertex covers for all edges assigned to the first i parties. An interesting consequence is that the communication cost of our protocol is O(n) bits, as opposed to the typical Ω(nlog n) bits required for many graph problems, such as maximum matching, where protocols commonly involve communicating edges.
Cite as

Mahsa Derakhshan, Andisheh Ghasemi, and Rajmohan Rajaraman. One-Way Communication Complexity of Minimum Vertex Cover in General Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 66:1-66:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{derakhshan_et_al:LIPIcs.ICALP.2025.66,
  author =	{Derakhshan, Mahsa and Ghasemi, Andisheh and Rajaraman, Rajmohan},
  title =	{{One-Way Communication Complexity of Minimum Vertex Cover in General Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{66:1--66:19},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-234430},
  doi =		{10.4230/LIPIcs.ICALP.2025.66},
  annote =	{Keywords: Communication Complexity, Minimum Vertex Cover}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.67
Query Efficient Weighted Stochastic Matching

Authors: Mahsa Derakhshan and Mohammad Saneian

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

Abstract
In this paper, we study the weighted stochastic matching problem. Let G = (V, E) be a given edge-weighted graph, and let its realization 𝒢 be a random subgraph of G that includes each edge e ∈ E independently with a known probability p_e. The goal in this problem is to pick a sparse subgraph Q of G without prior knowledge of 𝒢, such that the maximum weight matching among the realized edges of Q (i.e., the subgraph Q ∩ 𝒢) in expectation approximates the maximum weight matching of the entire realization 𝒢. It is established by previous work that attaining any constant approximation ratio for this problem requires selecting a subgraph of max-degree Ω(1/p), where p = min_{e ∈ E} p_e. On the positive side, there exists a (1-ε)-approximation algorithm by Behnezhad and Derakhshan [FOCS'20], albeit at the cost of a max-degree having exponential dependence on 1/p. Within the O(1/p) query regime, however, the best-known algorithm achieves a 0.536 approximation ratio due to Dughmi, Kalayci, and Patel [ICALP'23], improving over the 0.501 approximation algorithm by Behnezhad, Farhadi, Hajiaghayi, and Reyhani [SODA'19]. In this work, we present a 0.68-approximation algorithm with the asymptotically optimal O(1/p) queries per vertex. Our result not only substantially improves the approximation ratio for weighted graphs, but also breaks the well-known 2/3 barrier with the optimal number of queries - even for unweighted graphs. Our analysis involves reducing the problem to designing a randomized matching algorithm on a given stochastic graph with some variance-bounding properties. To achieve these properties, we leverage a randomized algorithm by MacRury and Ma [STOC'24] for a variant of online stochastic matching.
Cite as

Mahsa Derakhshan and Mohammad Saneian. Query Efficient Weighted Stochastic Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{derakhshan_et_al:LIPIcs.ICALP.2025.67,
  author =	{Derakhshan, Mahsa and Saneian, Mohammad},
  title =	{{Query Efficient Weighted Stochastic Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{67:1--67:20},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-234445},
  doi =		{10.4230/LIPIcs.ICALP.2025.67},
  annote =	{Keywords: Sublinear algorithms, Stochastic, Matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.6
String Problems in the Congested Clique Model

Authors: Shay Golan and Matan Kraus

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, n nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and the communication between the nodes is conducted in rounds. In each round, every node is allowed to send an O(log n)-bit message to every other node in the network. We consider three fundamental string problems in the Congested Clique model. First, we present an O(1) rounds algorithm for string sorting that supports strings of arbitrary length. Second, we present an O(1) rounds combinatorial pattern matching algorithm. Finally, we present an O(log log n) rounds algorithm for the computation of the suffix array and the corresponding Longest Common Prefix array of a given string.
Cite as

Shay Golan and Matan Kraus. String Problems in the Congested Clique Model. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{golan_et_al:LIPIcs.CPM.2025.6,
  author =	{Golan, Shay and Kraus, Matan},
  title =	{{String Problems in the Congested Clique Model}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.6},
  URN =		{urn:nbn:de:0030-drops-231003},
  doi =		{10.4230/LIPIcs.CPM.2025.6},
  annote =	{Keywords: String Sorting, Pattern Matching, Suffix Array, Congested Clique, Sorting}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.25
Local Density and Its Distributed Approximation

Authors: Aleksander Bjørn Christiansen, Ivor van der Hoog, and Eva Rotenberg

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

Abstract
The densest subgraph problem is a classic problem in combinatorial optimisation. Graphs with low maximum subgraph density are often called "uniformly sparse", leading to algorithms parameterised by this density. However, in reality, the sparsity of a graph is not necessarily uniform. This calls for a formally well-defined, fine-grained notion of density. Danisch, Chan, and Sozio propose a definition for local density that assigns to each vertex v a value ρ^*(v). This local density is a generalisation of the maximum subgraph density of a graph. I.e., if ρ(G) is the subgraph density of a finite graph G, then ρ(G) equals the maximum local density ρ^*(v) over vertices v in G. They present a Frank-Wolfe-based algorithm to approximate the local density of each vertex with no theoretical (asymptotic) guarantees. We provide an extensive study of this local density measure. Just as with (global) maximum subgraph density, we show that there is a dual relation between the local out-degrees and the minimum out-degree orientations of the graph. We introduce the definition of the local out-degree g^*(v) of a vertex v, and show it to be equal to the local density ρ^*(v). We consider the local out-degree to be conceptually simpler, shorter to define, and easier to compute. Using the local out-degree we show a previously unknown fact: that existing algorithms already dynamically approximate the local density for each vertex with polylogarithmic update time. Next, we provide the first distributed algorithms that compute the local density with provable guarantees: given any ε such that ε^{-1} ∈ O(poly n), we show a deterministic distributed algorithm in the LOCAL model where, after O(ε^{-2} log² n) rounds, every vertex v outputs a (1 + ε)-approximation of their local density ρ^*(v). In CONGEST, we show a deterministic distributed algorithm that requires poly(log n,ε^{-1}) ⋅ 2^{O(√{log n})} rounds, which is sublinear in n. As a corollary, we obtain the first deterministic algorithm running in a sublinear number of rounds for (1+ε)-approximate densest subgraph detection in the CONGEST model.
Cite as

Aleksander Bjørn Christiansen, Ivor van der Hoog, and Eva Rotenberg. Local Density and Its Distributed Approximation. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{christiansen_et_al:LIPIcs.STACS.2025.25,
  author =	{Christiansen, Aleksander Bj{\o}rn and van der Hoog, Ivor and Rotenberg, Eva},
  title =	{{Local Density and Its Distributed Approximation}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{25:1--25:20},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-228502},
  doi =		{10.4230/LIPIcs.STACS.2025.25},
  annote =	{Keywords: Distributed graph algorithms, graph density computation, graph density approximation, network analysis theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.41
Query Complexity of Stochastic Minimum Vertex Cover

Authors: Mahsa Derakhshan, Mohammad Saneian, and Zhiyang Xun

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We study the stochastic minimum vertex cover problem for general graphs. In this problem, we are given a graph G = (V, E) and an existence probability p_e for each edge e ∈ E. Edges of G are realized (or exist) independently with these probabilities, forming the realized subgraph 𝒢. The existence of an edge in 𝒢 can only be verified using edge queries. The goal of this problem is to find a near-optimal vertex cover of 𝒢 using a small number of queries. Previous work by Derakhshan, Durvasula, and Haghtalab [STOC 2023] established the existence of 1.5 + ε approximation algorithms for this problem with O(n/ε) queries. They also show that, under mild correlation among edge realizations, beating this approximation ratio requires querying a subgraph of size Ω(n ⋅ RS(n)). Here, RS(n) refers to Ruzsa-Szemerédi Graphs and represents the largest number of induced edge-disjoint matchings of size Θ(n) in an n-vertex graph. In this work, we design a simple algorithm for finding a (1 + ε) approximate vertex cover by querying a subgraph of size O(n ⋅ RS(n)) for any absolute constant ε > 0. Our algorithm can tolerate up to O(n ⋅ RS(n)) correlated edges, hence effectively completing our understanding of the problem under mild correlation.
Cite as

Mahsa Derakhshan, Mohammad Saneian, and Zhiyang Xun. Query Complexity of Stochastic Minimum Vertex Cover. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 41:1-41:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{derakhshan_et_al:LIPIcs.ITCS.2025.41,
  author =	{Derakhshan, Mahsa and Saneian, Mohammad and Xun, Zhiyang},
  title =	{{Query Complexity of Stochastic Minimum Vertex Cover}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{41:1--41:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.41},
  URN =		{urn:nbn:de:0030-drops-226691},
  doi =		{10.4230/LIPIcs.ITCS.2025.41},
  annote =	{Keywords: Sublinear algorithms, Vertex cover, Query complexity}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.36
Brief Announcement: Streaming and Massively Parallel Algorithms for Edge Coloring

Authors: Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Marina Knittel, and Hamed Saleh

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
A valid edge-coloring of a graph is an assignment of "colors" to its edges such that no two incident edges receive the same color. The goal is to find a proper coloring that uses few colors. In this paper, we revisit this problem in two models of computation specific to massive graphs, the Massively Parallel Computations (MPC) model and the Graph Streaming model: Massively Parallel Computation. We give a randomized MPC algorithm that w.h.p., returns a (1+o(1))Delta edge coloring in O(1) rounds using O~(n) space per machine and O(m) total space. The space per machine can also be further improved to n^{1-Omega(1)} if Delta = n^{Omega(1)}. This is, to our knowledge, the first constant round algorithm for a natural graph problem in the strongly sublinear regime of MPC. Our algorithm improves a previous result of Harvey et al. [SPAA 2018] which required n^{1+Omega(1)} space to achieve the same result. Graph Streaming. Since the output of edge-coloring is as large as its input, we consider a standard variant of the streaming model where the output is also reported in a streaming fashion. The main challenge is that the algorithm cannot "remember" all the reported edge colors, yet has to output a proper edge coloring using few colors. We give a one-pass O~(n)-space streaming algorithm that always returns a valid coloring and uses 5.44 Delta colors w.h.p., if the edges arrive in a random order. For adversarial order streams, we give another one-pass O~(n)-space algorithm that requires O(Delta^2) colors.
Cite as

Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Marina Knittel, and Hamed Saleh. Brief Announcement: Streaming and Massively Parallel Algorithms for Edge Coloring. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 36:1-36:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{behnezhad_et_al:LIPIcs.DISC.2019.36,
  author =	{Behnezhad, Soheil and Derakhshan, Mahsa and Hajiaghayi, MohammadTaghi and Knittel, Marina and Saleh, Hamed},
  title =	{{Brief Announcement: Streaming and Massively Parallel Algorithms for Edge Coloring}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{36:1--36:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.36},
  URN =		{urn:nbn:de:0030-drops-113438},
  doi =		{10.4230/LIPIcs.DISC.2019.36},
  annote =	{Keywords: Massively Parallel Computation, Streaming, Edge Coloring}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.15
Streaming and Massively Parallel Algorithms for Edge Coloring

Authors: Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Marina Knittel, and Hamed Saleh

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
A valid edge-coloring of a graph is an assignment of "colors" to its edges such that no two incident edges receive the same color. The goal is to find a proper coloring that uses few colors. (Note that the maximum degree, Delta, is a trivial lower bound.) In this paper, we revisit this fundamental problem in two models of computation specific to massive graphs, the Massively Parallel Computations (MPC) model and the Graph Streaming model: - Massively Parallel Computation: We give a randomized MPC algorithm that with high probability returns a Delta+O~(Delta^(3/4)) edge coloring in O(1) rounds using O(n) space per machine and O(m) total space. The space per machine can also be further improved to n^(1-Omega(1)) if Delta = n^Omega(1). Our algorithm improves upon a previous result of Harvey et al. [SPAA 2018]. - Graph Streaming: Since the output of edge-coloring is as large as its input, we consider a standard variant of the streaming model where the output is also reported in a streaming fashion. The main challenge is that the algorithm cannot "remember" all the reported edge colors, yet has to output a proper edge coloring using few colors. We give a one-pass O~(n)-space streaming algorithm that always returns a valid coloring and uses 5.44 Delta colors with high probability if the edges arrive in a random order. For adversarial order streams, we give another one-pass O~(n)-space algorithm that requires O(Delta^2) colors.
Cite as

Soheil Behnezhad, Mahsa Derakhshan, MohammadTaghi Hajiaghayi, Marina Knittel, and Hamed Saleh. Streaming and Massively Parallel Algorithms for Edge Coloring. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{behnezhad_et_al:LIPIcs.ESA.2019.15,
  author =	{Behnezhad, Soheil and Derakhshan, Mahsa and Hajiaghayi, MohammadTaghi and Knittel, Marina and Saleh, Hamed},
  title =	{{Streaming and Massively Parallel Algorithms for Edge Coloring}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.15},
  URN =		{urn:nbn:de:0030-drops-111361},
  doi =		{10.4230/LIPIcs.ESA.2019.15},
  annote =	{Keywords: Massively Parallel Computation, Streaming, Edge Coloring}
}
  • Refine by Type
  • 16 Document/PDF
  • 13 Document/HTML

  • Refine by Publication Year
  • 3 2026
  • 10 2025
  • 2 2019
  • 1 2018

  • Refine by Author
  • 6 Derakhshan, Mahsa
  • 3 Behnezhad, Soheil
  • 3 Hajiaghayi, MohammadTaghi
  • 2 Knittel, Marina
  • 2 Saleh, Hamed
  • Show More...

  • Refine by Series/Journal
  • 16 LIPIcs

  • Refine by Classification
  • 5 Theory of computation → Streaming, sublinear and near linear time algorithms
  • 3 Theory of computation → Massively parallel algorithms
  • 2 Theory of computation → Distributed algorithms
  • 2 Theory of computation → Graph algorithms analysis
  • 2 Theory of computation → Online algorithms
  • Show More...

  • Refine by Keyword
  • 3 Streaming
  • 2 Edge Coloring
  • 2 Massively Parallel Computation
  • 2 Sublinear algorithms
  • 1 Adaptive adversary
  • 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