51 Search Results for "Upfal, Eli"

Document
DOI: 10.4230/LIPIcs.SEA.2026.2
Different Scales of Randomness: Empirical Mixing Times of the Edge Switching and Curveball MCMC

Authors: Deepak Ajwani, Melvin Kallmayer, Alexander Leonhardt, Ulrich Meyer, Ryan O'Connor, and Manuel Penschuck

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
The Fixed Degree Sequence Model (FDSM) asks for a uniform sample from the set of all simple graphs that match a prescribed degree sequence. It is typically implemented using Markov-Chain Monte-Carlo (MCMC) processes, such as Edge Switching or Curveball (and their variants). Yet despite decades of research, rigorous bounds on the mixing times of such processes remain impractical. Consequently, several experimental techniques have been used to derive "empirical lower bounds" on the mixing time. We address the following research questions: (1) Which commonly studied graph-theoretic properties serve as reliable empirical predictors for mixing of FDSM MCMC processes? (2) At what structural scales do these properties operate primarily (i. e., are they predominantly local or global in nature)? (3) How can these properties be characterised and quantified most effectively? To this end, we propose Claim, a novel systematic method to establish empirical lower bounds using learnt classifiers, and compare it to existing methods. Apart from interesting insights into the usage of machine learning for this problem, we also derive robust graph properties with respect to different randomisation algorithms. Although experimental in nature, these results may influence both theorist’s and algorithm engineer’s work on improved bounds and better algorithm respectively.
Cite as

Deepak Ajwani, Melvin Kallmayer, Alexander Leonhardt, Ulrich Meyer, Ryan O'Connor, and Manuel Penschuck. Different Scales of Randomness: Empirical Mixing Times of the Edge Switching and Curveball MCMC. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ajwani_et_al:LIPIcs.SEA.2026.2,
  author =	{Ajwani, Deepak and Kallmayer, Melvin and Leonhardt, Alexander and Meyer, Ulrich and O'Connor, Ryan and Penschuck, Manuel},
  title =	{{Different Scales of Randomness: Empirical Mixing Times of the Edge Switching and Curveball MCMC}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.2},
  URN =		{urn:nbn:de:0030-drops-260062},
  doi =		{10.4230/LIPIcs.SEA.2026.2},
  annote =	{Keywords: Mixing Time, Graph Randomization, Machine Learning, Edge Switching}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.15
One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming

Authors: Avinandan Das

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
This paper investigates the semi-streaming complexity of k-partial coloring, a generalization of proper graph coloring. For k ≥ 1, a k-partial coloring requires that each vertex v in an n-node graph is assigned a color such that at least min{k, deg(v)} of its neighbors are assigned colors different from its own. This framework naturally extends classical coloring problems: specifically, k-partial (k+1)-coloring and k-partial k-coloring generalize (Δ+1)-proper coloring and Δ-proper coloring, respectively. Prior works of Assadi, Chen, and Khanna [SODA 2019] and Assadi, Kumar, and Mittal [TheoretiCS 2023] show that both (Δ+1)-proper coloring and Δ-proper coloring admit one-pass randomized semi-streaming algorithms. We explore whether these efficiency gains extend to their partial coloring generalizations and reveal a sharp computational threshold: while k-partial (k+1)-coloring admits a one-pass randomized semi-streaming algorithm, the k-partial k-coloring remains semi-streaming intractable, effectively demonstrating a "dichotomy of one color" in the streaming model.
Cite as

Avinandan Das. One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{das:LIPIcs.SWAT.2026.15,
  author =	{Das, Avinandan},
  title =	{{One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.15},
  URN =		{urn:nbn:de:0030-drops-260515},
  doi =		{10.4230/LIPIcs.SWAT.2026.15},
  annote =	{Keywords: Graph Coloring, Semi-streaming algorithms, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.28
Periodicity Property Testing on Strings with Wildcards

Authors: Carl Barton, Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Oded Lachish, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
In this work, we study periodicity in strings with wildcards. A string T with at most k wildcards is called strongly (p,k)-periodic if the wildcards in T can be replaced with alphabet symbols to obtain a string with period p, and weakly (p,k)-periodic if T[i] matches T[i+p] for all i. Intuitively, both generalize to (≤ g, k)-periodicity, which is the property of being (p,k)-periodic for some p ∈ [1..g]. An ε-tester for a property 𝒫 is an algorithm that distinguishes between strings that satisfy 𝒫 and strings where one needs to change at least an ε-fraction of the symbols to obtain a string that satisfies 𝒫. We study one-sided error testers, where strings satisfying 𝒫 must always be accepted, while strings that are ε-far must be rejected with probability at least 2/3. The complexity of a tester is the worst-case number of symbols of an input of length n it must read to make the decision. We design the following testers for p,g ≤ n/2: 1) An ε-tester for strong (p,k)-periodicity with complexity Õ_ε(1) . 2) An ε-tester for strong (≤ g,k)-periodicity with complexity Õ_ε(√g). 3) An ε-tester for weak (p,k)-periodicity with complexity Õ_ε(min(k, n /(k+p))). 4) An ε-tester for weak (≤ g,k)-periodicity with complexity Õ_ε(min(k+ √{gk}, n/√k)). Additionally, we show a lower bound on the complexity of ε-testers for weak (≤ g,k)-periodicity, implying that our tester for weak (≤ g,k)-periodicity is optimal up to a multiplicative (ε^{-1} ln(gk))^O(1) factor for a wide range of g and k. Finally, our tester for strong (≤ g,k)-periodicity generalizes the one of [Lachish and Newman; Algorithmica 2011] for strings without wildcards, matching (up to polylogarithmic factors) the unconditional lower bound of ̃Ω(√g) in said work for constant ε.
Cite as

Carl Barton, Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Oded Lachish, and Tatiana Starikovskaya. Periodicity Property Testing on Strings with Wildcards. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barton_et_al:LIPIcs.CPM.2026.28,
  author =	{Barton, Carl and Charalampopoulos, Panagiotis and Ghazi, Taha El and Ellert, Jonas and Lachish, Oded and Starikovskaya, Tatiana},
  title =	{{Periodicity Property Testing on Strings with Wildcards}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.28},
  URN =		{urn:nbn:de:0030-drops-259543},
  doi =		{10.4230/LIPIcs.CPM.2026.28},
  annote =	{Keywords: periodicity, property testing, wildcards}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.14
The Careless Coupon Collector’s Problem

Authors: Emilio Cruciani and Aditi Dudeja

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We initiate the study of the Careless Coupon Collector’s Problem (CCCP), a novel variation of the classical coupon collector, that we envision as a model for information systems such as web crawlers, dynamic caches, and fault-resilient networks. In CCCP, a collector attempts to gather n distinct coupon types by obtaining one coupon type uniformly at random in each discrete round, however the collector is careless: at the end of each round, each collected coupon type is independently lost with probability p. We analyze the number of rounds required to complete the collection as a function of n and p. In particular, we show that it transitions from Θ(n ln n) when p = o((ln n)/n²) up to Θ(((np)/(1-p))ⁿ) when p = ω(1/n) in multiple distinct phases. Interestingly, when p = c/n, the process remains in a metastable phase, where the fraction of collected coupon types is concentrated around 1/(1+c) with probability 1-o(1), for a time window of length e^{Θ(n)}. Finally, we give an algorithm that computes the expected completion time of CCCP in O(n²) time.
Cite as

Emilio Cruciani and Aditi Dudeja. The Careless Coupon Collector’s Problem. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cruciani_et_al:LIPIcs.FUN.2026.14,
  author =	{Cruciani, Emilio and Dudeja, Aditi},
  title =	{{The Careless Coupon Collector’s Problem}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.14},
  URN =		{urn:nbn:de:0030-drops-257333},
  doi =		{10.4230/LIPIcs.FUN.2026.14},
  annote =	{Keywords: Coupon Collector, Markov Chains, Metastability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.38
Fully Dynamic Spectral Sparsification for Directed Hypergraphs

Authors: Sebastian Forster, Gramoz Goranci, and Ali Momeni

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph sparsifiers of directed hypergraphs. Our algorithm achieves a near-optimal size of O(n² / ε ² log ⁷ m) and amortized update time of O(r² log ³ m), where n is the number of vertices, and m and r respectively upper bound the number of hyperedges and the rank of the hypergraph at any time. We also extend our approach to the parallel batch-dynamic setting, where a batch of any k hyperedge insertions or deletions can be processed with O(kr² log ³ m) amortized work and O(log ² m) depth. This constitutes the first spectral-based sparsification algorithm in this setting.
Cite as

Sebastian Forster, Gramoz Goranci, and Ali Momeni. Fully Dynamic Spectral Sparsification for Directed Hypergraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{forster_et_al:LIPIcs.STACS.2026.38,
  author =	{Forster, Sebastian and Goranci, Gramoz and Momeni, Ali},
  title =	{{Fully Dynamic Spectral Sparsification for Directed Hypergraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{38:1--38:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.38},
  URN =		{urn:nbn:de:0030-drops-255272},
  doi =		{10.4230/LIPIcs.STACS.2026.38},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.6
Threshold-Driven Streaming Graph: Expansion and Rumor Spreading

Authors: Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
A randomized distributed algorithm called RAES was introduced in [Becchetti et al., 2020] to extract a bounded-degree expander from a dense n-vertex expander graph G = (V, E). The algorithm relies on a simple threshold-based procedure. A key assumption in [Becchetti et al., 2020] is that the input graph G is static - i.e., both its vertex set V and edge set E remain unchanged throughout the process - while the analysis of raes in dynamic models is left as a major open question. In this work, we investigate the behavior of RAES under a dynamic graph model induced by a streaming node-churn process (also known as the sliding window model), where, at each discrete round, a new node joins the graph and the oldest node departs. This process yields a bounded-degree dynamic graph 𝒢 = {G_t = (V_t, E_t) : t ∈ ℕ} that captures essential characteristics of peer-to-peer networks - specifically, node churn and threshold on the number of connections each node can manage. We prove that every snapshot G_t in the dynamic graph sequence has good expansion properties with high probability. Furthermore, we leverage this property to establish a logarithmic upper bound on the completion time of the well-known PUSH and PULL rumor spreading protocols over the dynamic graph 𝒢.
Cite as

Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi. Threshold-Driven Streaming Graph: Expansion and Rumor Spreading. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{angileri_et_al:LIPIcs.STACS.2026.6,
  author =	{Angileri, Flora and Clementi, Andrea and Natale, Emanuele and Salvi, Michele and Ziccardi, Isabella},
  title =	{{Threshold-Driven Streaming Graph: Expansion and Rumor Spreading}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle 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.2026.6},
  URN =		{urn:nbn:de:0030-drops-254957},
  doi =		{10.4230/LIPIcs.STACS.2026.6},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Dynamic Random Graphs, Graph Expansion, Rumor Spreading}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.40
A Simple and Robust Protocol for Distributed Counting

Authors: Edith Cohen, Moshe Shechner, and Uri Stemmer

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

Abstract
We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across k sites while minimizing communication. The communication complexity of this problem is known to be Θ(k/(ε)log N) for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to Θ((√k)/ε log N), but their analysis is restricted to the oblivious setting, where the stream of events is independent of the protocol’s outputs. Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a polylog(k) factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust? We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of O((√k)/ε log N). Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.
Cite as

Edith Cohen, Moshe Shechner, and Uri Stemmer. A Simple and Robust Protocol for Distributed Counting. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 40:1-40:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2026.40,
  author =	{Cohen, Edith and Shechner, Moshe and Stemmer, Uri},
  title =	{{A Simple and Robust Protocol for Distributed Counting}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{40:1--40:24},
  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.2026.40},
  URN =		{urn:nbn:de:0030-drops-253272},
  doi =		{10.4230/LIPIcs.ITCS.2026.40},
  annote =	{Keywords: Distributed Streaming, Adversarial Streaming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.63
Perfect Simulation of Las Vegas Algorithms via Local Computation

Authors: Xinyu Fu, Yonggang Jiang, and Yitong Yin

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

Abstract
The notion of Las Vegas algorithms was introduced by Babai (1979) and can be defined in two ways: - In Babai’s original definition, a randomized algorithm is called Las Vegas if it has a finitely bounded running time and certifiable random failure. - Another definition widely accepted today is that Las Vegas algorithms refer to zero-error randomized algorithms with random running times. The equivalence between the two definitions is straightforward. Specifically, for randomized algorithms with certifiable failures, repeatedly running the algorithm until no failure is encountered allows for faithful simulation of the correct output when it executes successfully. We show that a similar perfect simulation can also be achieved in distributed local computation. Specifically, in the LOCAL model, with a polylogarithmic overhead in time complexity, any Las Vegas algorithm with finitely bounded running time and locally certifiable failures can be converted to a zero error Las Vegas algorithm. This transformed algorithm faithfully reproduces the correct output of the original algorithm in successful executions. This is achieved by a reduction to a distributed sampling problem under the Lovász Local Lemma (LLL), where the objective is to sample from the joint distribution of random variables avoiding all bad events. We then design the first efficient algorithm to solve this sampling problem in the LOCAL model.
Cite as

Xinyu Fu, Yonggang Jiang, and Yitong Yin. Perfect Simulation of Las Vegas Algorithms via Local Computation. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fu_et_al:LIPIcs.ITCS.2026.63,
  author =	{Fu, Xinyu and Jiang, Yonggang and Yin, Yitong},
  title =	{{Perfect Simulation of Las Vegas Algorithms via Local Computation}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{63:1--63:22},
  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.2026.63},
  URN =		{urn:nbn:de:0030-drops-253503},
  doi =		{10.4230/LIPIcs.ITCS.2026.63},
  annote =	{Keywords: Las Vegas algorithms, perfect simulation, Lov\'{a}sz Local Lemma, sampling}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.107
New Greedy Spanners and Applications

Authors: Elizaveta Popova and Elad Tzalik

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

Abstract
We present a simple greedy procedure to compute an (α,β)-spanner for a graph G. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is an algorithm that, given a multigraph G, outputs an f edge fault-tolerant (k,k-1)-spanner H of size O(fn^{1+1/k}) which is tight. To our knowledge, this is the first tight result concerning the price of fault tolerance in spanners which are not multiplicative, in any model of faults. Our second main result is a new construction of a spanner for weighted graphs. We show that any weighted graph G has a subgraph H with O(n^{1+1/k}) edges such that any path P of hop-length 𝓁 in G has a replacement path P' in H of weighted length ≤ w(P)+(2k-2)w^(1/2)(P) where w(P) is the total edge weight of P, and w^(1/2) denotes the sum of the largest ⌈𝓁/2⌉ edge weights along P. Moreover, we show such approximation is optimal for shortest paths of hop-length 2. To our knowledge, this is the first construction of a "spanner" for weighted graphs that strictly improves upon the stretch of multiplicative (2k-1)-spanners for all non-adjacent vertex pairs, while maintaining the same size bound. Our technique is based on using clustering and ball-growing, which are methods commonly used in designing spanner algorithms, to analyze simple greedy algorithms. This allows us to combine the flexibility of clustering approaches with the unique properties of the greedy algorithm to get improved bounds. In particular, our methods give a very short proof that the parallel greedy spanner adds O(kn^{1+1/k}) edges, improving upon known bounds.
Cite as

Elizaveta Popova and Elad Tzalik. New Greedy Spanners and Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 107:1-107:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{popova_et_al:LIPIcs.ITCS.2026.107,
  author =	{Popova, Elizaveta and Tzalik, Elad},
  title =	{{New Greedy Spanners and Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{107:1--107:25},
  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.2026.107},
  URN =		{urn:nbn:de:0030-drops-253945},
  doi =		{10.4230/LIPIcs.ITCS.2026.107},
  annote =	{Keywords: Graph Spanners, Greedy Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.102
Smoothed Analysis of Dynamic Graph Algorithms

Authors: Uri Meir and Ami Paz

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

Abstract
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and Yu, FOCS 2023). As worst-case analysis (adversarial inputs) may lead to the necessity of high running times, a natural question arises: in which cases are high running times really necessary, and in which cases these inputs merely manifest unique pathological cases? Early attempts to tackle this question were made by Nikoletseas, Reif, Spirakis and Yung (ICALP 1995) and by Alberts and Henzinger (Algorithmica 1998), who considered models with very little adversarial control over the inputs, and showed fast algorithms exist for them. The question was then overlooked for decades, until Henzinger, Lincoln and Saha (SODA 2022) recently addressed uniformly random inputs, and presented algorithms and impossibility results for several subgraph counting problems. To tackle the above question more thoroughly, we employ smoothed analysis, a celebrated framework introduced by Spielman and Teng (J. ACM, 2004). An input is proposed by an adversary but then a noisy version of it is processed by the algorithm instead. This model of inputs is parameterized by the amount of adversarial control, and fully interpolates between worst-case inputs and a uniformly random input. Doing so, we extend impossibility results for some problems to the smoothed model with only a minor quantitative loss. That is, we show that partially-adversarial inputs suffice to impose high running times for certain problems. In contrast, we show that other problems become easy even with the slightest amount of noise. In addition, we study the interplay between the adversary and the noise, leading to three natural models of smoothed inputs, for which we show a hierarchy of increasing difficulty stretching between the average-case and the worst-case complexities.
Cite as

Uri Meir and Ami Paz. Smoothed Analysis of Dynamic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{meir_et_al:LIPIcs.ITCS.2026.102,
  author =	{Meir, Uri and Paz, Ami},
  title =	{{Smoothed Analysis of Dynamic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{102:1--102:20},
  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.2026.102},
  URN =		{urn:nbn:de:0030-drops-253896},
  doi =		{10.4230/LIPIcs.ITCS.2026.102},
  annote =	{Keywords: Dynamic graph algorithms, Smoothed analysis, Shortest paths}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.30
Byzantine-Tolerant Phase Clock

Authors: Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
A phase clock is a basic synchronization mechanism that keeps distributed nodes closely synchronized to execute the same phase of a distributed algorithm. A phase clock is typically implemented with a local logical counter that keeps track of the current phase count. Phase clocks are particularly useful in population protocols for implementing leader election and majority selection. We study phase clocks that tolerate Byzantine faults. We show that there is a phase clock that tolerates up to f < n/3 faulty nodes, where n is the number of nodes, such that the gap of the local counter values is O(n²log n). The gap can be further lowered to O(log n) when f ≤ n/8. We also show that if f > n/3, then the gap grows to infinity as time increases. While analyzing phase clock we introduce novel techniques and bounds for balls into bins processes, which might be of independent interest. Using the phase clock, we obtain a majority selection population protocol that tolerates up to f faults and decides on the majority value in O(log² n) parallel time using poly-log states per node.
Cite as

Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski. Byzantine-Tolerant Phase Clock. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{busch_et_al:LIPIcs.OPODIS.2025.30,
  author =	{Busch, Costas and Garncarek, Pawe{\l} and Kowalski, Dariusz R.},
  title =	{{Byzantine-Tolerant Phase Clock}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.30},
  URN =		{urn:nbn:de:0030-drops-252036},
  doi =		{10.4230/LIPIcs.OPODIS.2025.30},
  annote =	{Keywords: phase clock, Byzantine nodes, population protocols, balls into bins}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.23
Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes

Authors: Archit Chauhan, Samir Datta, and M. Praveen

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deterministic NC algorithms for DFS in planar graphs and digraphs. We further extend these results to more general graph classes, by providing NC algorithms for (di)graphs of bounded genus, and for undirected H-minor-free graphs where H is a fixed graph with at most one crossing. For the case of (di)graphs of bounded treewidth, we further improve the complexity to a Logspace bound. Constructing a maximal path is a simpler problem (that reduces to DFS) for which no deterministic parallel bounds are known for general graphs. For planar graphs a bound of O(log n) parallel time on a CRCW PRAM (thus in NC²) is known. We improve this bound to Logspace.
Cite as

Archit Chauhan, Samir Datta, and M. Praveen. Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chauhan_et_al:LIPIcs.FSTTCS.2025.23,
  author =	{Chauhan, Archit and Datta, Samir and Praveen, M.},
  title =	{{Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.23},
  URN =		{urn:nbn:de:0030-drops-251041},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.23},
  annote =	{Keywords: Parallel Complexity, Graph Algorithms, Depth First Search, Maximal Path, Planar Graphs, Minor-Free, Treewidth, Logspace}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.21
Overlay Network Construction: Improved Overall and Node-Wise Message Complexity

Authors: Yi-Jun Chang, Yanyu Chen, and Gopinath Mishra

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We consider the problem of constructing distributed overlay networks, where nodes in a reconfigurable system can create or sever connections with nodes whose identifiers they know. Initially, each node knows only its own and its neighbors' identifiers, forming a local channel, while the evolving structure is termed the global channel. The goal is to reconfigure any connected graph into a desired topology, such as a bounded-degree expander graph or a well-formed tree (WFT) with a constant maximum degree and logarithmic diameter, minimizing the total number of rounds and message complexity. This problem mirrors real-world peer-to-peer network construction, where creating robust and efficient systems is desired. We study the overlay reconstruction problem in a network of n nodes in two models: GOSSIP-reply and HYBRID. In the GOSSIP-reply model, each node can send a message and receive a corresponding reply message in one round. In the HYBRID model, a node can send O(1) messages to each neighbor in the local channel and a total of O(log n) messages in the global channel. In both models, we propose protocols for WFT construction with O (n log n) message complexities using messages of O(log n) bits. In the GOSSIP-reply model, our protocol takes O(log n) rounds while in the HYBRID model, our protocol takes O(log² n) rounds. Both protocols use O (n log² n) bits of communication. We obtain improved bounds over prior work: GOSSIP-reply: A recent result by Dufoulon et al. (ITCS 2024) achieved O(log⁵ n) round complexity and O (n log⁵ n) message complexity using messages of at least Ω(log² n) bits in GOSSIP-reply. With messages of size O(log n), our protocol achieves an optimal round complexity of O(log n) and an improved message complexity of O(n log n). HYBRID: Götte et al. (Distributed Computing 2023) showed an optimal O(log n)-round algorithm with O(log² n) global messages per round which incurs a message complexity of Ω(m), where m is the number of edges in the initial topology. At the cost of increasing the round complexity to O(log² n) while using only O(log n) messages globally, our protocol achieves a message complexity that is independent of m. Our approach ensures that the total number of messages for node v, with degree deg(v) in the initial topology, is bounded by O(deg(v) + log n), while the algorithm of Götte et al. requires O(deg(v) + (log⁴ n)/(log log n)) messages per node.
Cite as

Yi-Jun Chang, Yanyu Chen, and Gopinath Mishra. Overlay Network Construction: Improved Overall and Node-Wise Message Complexity. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chang_et_al:LIPIcs.FSTTCS.2025.21,
  author =	{Chang, Yi-Jun and Chen, Yanyu and Mishra, Gopinath},
  title =	{{Overlay Network Construction: Improved Overall and Node-Wise Message Complexity}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{21:1--21:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-251025},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.21},
  annote =	{Keywords: Distributed algorithms, Overlay networks, Expander graphs}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.38
Compact Routing Schemes in Undirected and Directed Graphs

Authors: Avi Kadria and Liam Roditty

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In this paper, we study the problem of compact routing schemes in weighted undirected and directed graphs. For weighted undirected graphs, more than a decade ago, Chechik [PODC'13] presented a ≈ 3.68k-stretch compact routing scheme that uses Õ(n^{1/k}log{D}) local storage, where D is the normalized diameter, for every k > 1. We present a ≈ 2.64k-stretch compact routing scheme that uses Õ(n^{1/k}) local storage on average in each vertex. This is the first compact routing scheme that uses total local storage of Õ(n^{1+1/k}) while achieving a c ⋅ k stretch, for a constant c < 3. In real-world network protocols, messages are usually transmitted as part of a communication session between two parties. Therefore, more than two decades ago, Thorup and Zwick [SPAA'01] considered compact routing schemes that establish a communication session using a handshake. In their handshake-based compact routing scheme, the handshake is routed along a (4k-5)-stretch path, and the rest of the communication session is routed along an optimal (2k-1)-stretch path. It is straightforward to improve the (4k-5)-stretch of the handshake to ≈ 3.68k-stretch using the compact routing scheme of Chechik [PODC'13]. We improve the handshake stretch to the optimal (2k-1), by borrowing the concept of roundtrip routing from directed graphs to undirected graphs. For weighted directed graphs, more than two decades ago, Roditty, Thorup, and Zwick [SODA'02 and TALG'08] presented a (4k+ε)-stretch compact roundtrip routing scheme that uses Õ(n^{1/k}) local storage for every k ≥ 3. For k = 3, this gives a (12+ε)-roundtrip stretch using Õ(n^{1/3}) local storage. We improve the stretch by developing a 7-roundtrip stretch routing scheme with Õ(n^{1/3}) local storage. In addition, we consider graphs with bounded hop diameter and present an optimal (2k-1)-roundtrip stretch routing scheme that uses Õ(D_{HOP}⋅ n^{1/k}), where D_{HOP} is the hop diameter of the graph.
Cite as

Avi Kadria and Liam Roditty. Compact Routing Schemes in Undirected and Directed Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kadria_et_al:LIPIcs.DISC.2025.38,
  author =	{Kadria, Avi and Roditty, Liam},
  title =	{{Compact Routing Schemes in Undirected and Directed Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{38:1--38:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.38},
  URN =		{urn:nbn:de:0030-drops-248555},
  doi =		{10.4230/LIPIcs.DISC.2025.38},
  annote =	{Keywords: Routing schemes, Compact routing schemes, Distance oracles, Computer networks, Graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.26
Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders

Authors: Emilio Cruciani, Sebastian Forster, and Tijn de Vos

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We study a multi-call variant of the classic PUSH&PULL rumor spreading process where nodes can contact k of their neighbors instead of a single one during both PUSH and PULL operations. We show that rumor spreading can be made faster at the cost of an increased amount of communication between the nodes. As a motivating example, consider the process on a complete graph of n nodes: while the standard PUSH&PULL protocol takes Θ(log n) rounds, we prove that our k-PUSH&PULL variant completes in Θ(log_{k} n) rounds, with high probability. We generalize this result in an expansion-sensitive way, as has been done for the classic PUSH&PULL protocol for different notions of expansion, e.g., conductance and vertex expansion. We consider small-set vertex expanders, graphs in which every sufficiently small subset of nodes has a large neighborhood, ensuring strong local connectivity. In particular, when the expansion parameter satisfies ϕ > 1, these graphs have a diameter of o(log n), as opposed to other standard notions of expansion. Since the graph’s diameter is a lower bound on the number of rounds required for rumor spreading, this makes small-set expanders particularly well-suited for fast information dissemination. We prove that k-PUSH&PULL takes O(log_{ϕ} n ⋅ log_{k} n) rounds in these expanders, with high probability. We complement this with a simple lower bound of Ω(log_{ϕ} n+ log_{k} n) rounds.
Cite as

Emilio Cruciani, Sebastian Forster, and Tijn de Vos. Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 26:1-26:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cruciani_et_al:LIPIcs.DISC.2025.26,
  author =	{Cruciani, Emilio and Forster, Sebastian and de Vos, Tijn},
  title =	{{Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{26:1--26:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.26},
  URN =		{urn:nbn:de:0030-drops-248434},
  doi =		{10.4230/LIPIcs.DISC.2025.26},
  annote =	{Keywords: small set expansion, vertex expansion, rumor spreading, multi-call rumor spreading, push\&pull protocol}
}
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