8 Search Results for "Karbasi, Amin"

Document
DOI: 10.4230/LIPIcs.ESA.2025.100
Cut-Query Algorithms with Few Rounds

Authors: Yotam Kenneth-Mordoch and Robert Krauthgamer

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

Abstract
In the cut-query model, the algorithm can access the input graph G = (V,E) only via cut queries that report, given a set S ⊆ V, the total weight of edges crossing the cut between S and V⧵ S. This model was introduced by Rubinstein, Schramm and Weinberg [ITCS'18] and its investigation has so far focused on the number of queries needed to solve optimization problems, such as global minimum cut. We turn attention to the round complexity of cut-query algorithms, and show that several classical problems can be solved in this model with only a constant number of rounds. Our main results are algorithms for finding a minimum cut in a graph, that offer different tradeoffs between round complexity and query complexity, where n = |V| and δ(G) denotes the minimum degree of G: (i) Õ(n^{4/3}) cut queries in two rounds in unweighted graphs; (ii) Õ(rn^{1+1/r}/δ(G)^{1/r}) queries in 2r+1 rounds for any integer r ≥ 1 again in unweighted graphs; and (iii) Õ(rn^{1+(1+log_n W)/r}) queries in 4r+3 rounds for any r ≥ 1 in weighted graphs. We also provide algorithms that find a minimum (s,t)-cut and approximate the maximum cut in a few rounds.
Cite as

Yotam Kenneth-Mordoch and Robert Krauthgamer. Cut-Query Algorithms with Few Rounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 100:1-100:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kennethmordoch_et_al:LIPIcs.ESA.2025.100,
  author =	{Kenneth-Mordoch, Yotam and Krauthgamer, Robert},
  title =	{{Cut-Query Algorithms with Few Rounds}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{100:1--100:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.100},
  URN =		{urn:nbn:de:0030-drops-245692},
  doi =		{10.4230/LIPIcs.ESA.2025.100},
  annote =	{Keywords: Cut Queries, Round Complexity, Submodular Optimization}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.50
Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries

Authors: Tatsuya Terao

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In the matroid intersection problem, we are given two matroids ℳ₁ = (V, ℐ₁) and ℳ₂ = (V, ℐ₂) defined on the same ground set V of n elements, and the objective is to find a common independent set S ∈ ℐ₁ ∩ ℐ₂ of largest possible cardinality, denoted by r. In this paper, we consider a deterministic matroid intersection algorithm with only a nearly linear number of independence oracle queries. Our contribution is to present a deterministic O(n/(ε) + r log r)-independence-query (2/3-ε)-approximation algorithm for any ε > 0. Our idea is very simple: we apply a recent Õ(n √r/ε)-independence-query (1 - ε)-approximation algorithm of Blikstad [ICALP 2021], but terminate it before completion. Moreover, we also present a semi-streaming algorithm for (2/3 -ε)-approximation of matroid intersection in O(1/ε) passes.
Cite as

Tatsuya Terao. Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{terao:LIPIcs.WADS.2025.50,
  author =	{Terao, Tatsuya},
  title =	{{Deterministic (2/3 - \epsilon)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.50},
  URN =		{urn:nbn:de:0030-drops-242812},
  doi =		{10.4230/LIPIcs.WADS.2025.50},
  annote =	{Keywords: Matroid intersection, approximation algorithm, streaming algorithm}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.19
GreedyML: A Parallel Algorithm for Maximizing Constrained Submodular Functions

Authors: Shivaram Gopal, S M Ferdous, Alex Pothen, and Hemanta Maji

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems on massive data sets, for practical contexts such as data summarization, machine learning, and graph sparsification. Our work builds on the randomized distributed RandGreeDI algorithm, proposed by Barbosa, Ene, Nguyen, and Ward (2015). This algorithm computes a distributed solution by randomly partitioning the data among all the processors and then employing a single accumulation step in which all processors send their partial solutions to one processor. However, for large problems, the accumulation step exceeds the memory available on a processor, and the processor which performs the accumulation becomes a computational bottleneck. Hence we propose a generalization of the RandGreeDI algorithm that employs multiple accumulation steps to reduce the memory required. We analyze the approximation ratio and the time complexity of the algorithm (in the BSP model). We evaluate the new GreedyML algorithm on three classes of problems, and report results from large-scale data sets with millions of elements. The results show that the GreedyML algorithm can solve problems where the sequential Greedy and distributed RandGreeDI algorithms fail due to memory constraints. For certain computationally intensive problems, the GreedyML algorithm is faster than the RandGreeDI algorithm. The observed approximation quality of the solutions computed by the GreedyML algorithm closely matches those obtained by the RandGreeDI algorithm on these problems.
Cite as

Shivaram Gopal, S M Ferdous, Alex Pothen, and Hemanta Maji. GreedyML: A Parallel Algorithm for Maximizing Constrained Submodular Functions. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gopal_et_al:LIPIcs.SEA.2025.19,
  author =	{Gopal, Shivaram and Ferdous, S M and Pothen, Alex and Maji, Hemanta},
  title =	{{GreedyML: A Parallel Algorithm for Maximizing Constrained Submodular Functions}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra 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.SEA.2025.19},
  URN =		{urn:nbn:de:0030-drops-232572},
  doi =		{10.4230/LIPIcs.SEA.2025.19},
  annote =	{Keywords: Combinatorial optimization, submodular functions, distributed algorithms, approximation algorithms, data summarization}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.19
Dynamic Algorithms for Submodular Matching

Authors: Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh

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

Abstract
The Maximum Submodular Matching (MSM) problem is a generalization of the classical Maximum Weight Matching (MWM) problem. In this problem, given a monotone submodular function f: 2^E → ℝ^{≥ 0} defined over subsets of edges of a graph G(V, E), we are asked to return a matching whose submodular value is maximum among all matchings in graph G(V, E). In this paper, we consider this problem in a fully dynamic setting against an oblivious adversary. In this setting, we are given a sequence 𝒮 of insertions and deletions of edges of the underlying graph G(V, E), along with an oracle access to the monotone submodular function f. The goal is to maintain a matching M such that, at any time t of sequence 𝒮, its submodular value is a good approximation of the value of the optimal submodular matching while keeping the number of operations minimal. We develop the first dynamic algorithm for the submodular matching problem, in which we maintain a matching whose submodular value is within expected (8 + ε)-approximation of the optimal submodular matching at any time t of sequence 𝒮 using expected amortized poly(log n, 1/(ε)) update time. Our approach incorporates a range of novel techniques, notably the concept of Uniform Hierarchical Caches (UHC) data structure along with its invariants, which lead to the first algorithm for fully dynamic submodular matching and may be of independent interest for designing dynamic algorithms for other problems.
Cite as

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh. Dynamic Algorithms for Submodular Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ICALP.2025.19,
  author =	{Banihashem, Kiarash and Biabani, Leyla and Goudarzi, Samira and Hajiaghayi, MohammadTaghi and Jabbarzade, Peyman and Monemizadeh, Morteza},
  title =	{{Dynamic Algorithms for Submodular Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-233969},
  doi =		{10.4230/LIPIcs.ICALP.2025.19},
  annote =	{Keywords: Matching, Submodular, Dynamic, Polylogarithmic}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.89
Optimal Communication Complexity of Chained Index

Authors: Janani Sundaresan

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

Abstract
We study the chain communication problem introduced by Cormode et al. [ICALP 2019]. For k ≥ 1, in the chain_{n,k} problem, there are k string and index pairs (X_i, σ_i) for i ∈ [k] such that the value at position σ_i in string X_i is the same bit for all k pairs. The input is shared between k+1 players as follows. Player 1 has the first string X₁ ∈ {0,1}ⁿ, player 2 has the first index σ₁ ∈ [n] and the second string X₂ ∈ {0,1}ⁿ, player 3 has the second index σ₂ ∈ [n] along with the third string X₃ ∈ {0,1}ⁿ, and so on. Player k+1 has the last index σ_k ∈ [n]. The communication is one way from each player to the next, starting from player 1 to player 2, then from player 2 to player 3 and so on. Player k+1, after receiving the message from player k, has to output a single bit which is the value at position σ_i in X_i for any i ∈ [k]. It is a generalization of the well-studied index problem, which is equivalent to chain_{n, 2}. Cormode et al. proved that the chain_{n,k} problem requires Ω(n/k²) communication, and they used it to prove streaming lower bounds for the approximation of maximum independent sets. Subsequently, Feldman et al. [STOC 2020] used it to prove lower bounds for streaming submodular maximization. However, it is not known whether the Ω(n/k²) lower bound used in these works is optimal for the problem, and in fact, it was conjectured by Cormode et al. that Ω(n) bits are necessary. We prove the optimal lower bound of Ω(n) for chain_{n,k} when k = o(n/log n) as our main result. This settles the open conjecture of Cormode et al., barring the range of k = Ω(n /log n). The main technique is a reduction to a non-standard index problem where the input to the players is such that the answer is biased away from uniform. This biased version of index is analyzed using tools from information theory. As a corollary, we get an improved lower bound for approximation of maximum independent set in vertex arrival streams via a reduction from chain directly.
Cite as

Janani Sundaresan. Optimal Communication Complexity of Chained Index. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 89:1-89:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sundaresan:LIPIcs.ITCS.2025.89,
  author =	{Sundaresan, Janani},
  title =	{{Optimal Communication Complexity of Chained Index}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{89:1--89:18},
  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.2025.89},
  URN =		{urn:nbn:de:0030-drops-227172},
  doi =		{10.4230/LIPIcs.ITCS.2025.89},
  annote =	{Keywords: communication complexity, index communciation problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.38
Backdoor Defense, Learnability and Obfuscation

Authors: Paul Christiano, Jacob Hilton, Victor Lecomte, and Mark Xu

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

Abstract
We introduce a formal notion of defendability against backdoors using a game between an attacker and a defender. In this game, the attacker modifies a function to behave differently on a particular input known as the "trigger", while behaving the same almost everywhere else. The defender then attempts to detect the trigger at evaluation time. If the defender succeeds with high enough probability, then the function class is said to be defendable. The key constraint on the attacker that makes defense possible is that the attacker’s strategy must work for a randomly-chosen trigger. Our definition is simple and does not explicitly mention learning, yet we demonstrate that it is closely connected to learnability. In the computationally unbounded setting, we use a voting algorithm of [Hanneke et al., 2022] to show that defendability is essentially determined by the VC dimension of the function class, in much the same way as PAC learnability. In the computationally bounded setting, we use a similar argument to show that efficient PAC learnability implies efficient defendability, but not conversely. On the other hand, we use indistinguishability obfuscation to show that the class of polynomial size circuits is not efficiently defendable. Finally, we present polynomial size decision trees as a natural example for which defense is strictly easier than learning. Thus, we identify efficient defendability as a notable intermediate concept in between efficient learnability and obfuscation.
Cite as

Paul Christiano, Jacob Hilton, Victor Lecomte, and Mark Xu. Backdoor Defense, Learnability and Obfuscation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{christiano_et_al:LIPIcs.ITCS.2025.38,
  author =	{Christiano, Paul and Hilton, Jacob and Lecomte, Victor and Xu, Mark},
  title =	{{Backdoor Defense, Learnability and Obfuscation}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{38:1--38:21},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-226662},
  doi =		{10.4230/LIPIcs.ITCS.2025.38},
  annote =	{Keywords: backdoors, machine learning, PAC learning, indistinguishability obfuscation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.46
Data-Driven Solution Portfolios

Authors: Marina Drygala, Silvio Lattanzi, Andreas Maggiori, Miltiadis Stouras, Ola Svensson, and Sergei Vassilvitskii

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

Abstract
In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select k potential solutions, with the goal of optimizing the value of the best solution. More formally, given a combinatorial problem Π, a set of value functions 𝒱 over the solutions of Π, and a distribution 𝒟 over 𝒱, our goal is to select k solutions of Π that maximize or minimize the expected value of the best of those solutions. For a simple example, consider the classic knapsack problem: given a universe of elements each with unit weight and a positive value, the task is to select r elements maximizing the total value. Now suppose that each element’s weight comes from a (known) distribution. How should we select k different solutions so that one of them is likely to yield a high value? In this work, we tackle this basic problem, and generalize it to the setting where the underlying set system forms a matroid. On the technical side, it is clear that the candidate solutions we select must be diverse and anti-correlated; however, it is not clear how to do so efficiently. Our main result is a polynomial-time algorithm that constructs a portfolio within a constant factor of the optimal.
Cite as

Marina Drygala, Silvio Lattanzi, Andreas Maggiori, Miltiadis Stouras, Ola Svensson, and Sergei Vassilvitskii. Data-Driven Solution Portfolios. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{drygala_et_al:LIPIcs.ITCS.2025.46,
  author =	{Drygala, Marina and Lattanzi, Silvio and Maggiori, Andreas and Stouras, Miltiadis and Svensson, Ola and Vassilvitskii, Sergei},
  title =	{{Data-Driven Solution Portfolios}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{46:1--46:15},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-226740},
  doi =		{10.4230/LIPIcs.ITCS.2025.46},
  annote =	{Keywords: solution portfolios, data-driven algorithm design, matroids}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.550
Constrained Binary Identification Problem

Authors: Amin Karbasi and Morteza Zadimoghaddam

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
We consider the problem of building a binary decision tree, to locate an object within a set by way of the least number of membership queries. This problem is equivalent to the "20 questions game" of information theory and is closely related to lossless source compression. If any query is admissible, Huffman coding is optimal with close to H[P] questions on average, the entropy of the prior distribution P over objects. However, in many realistic scenarios, there are constraints on which queries can be asked, and solving the problem optimally is NP-hard. We provide novel polynomial time approximation algorithms where constraints are defined in terms of "graph", general "cost", and "submodular" functions. In particular, we show that under graph constraints, there exists a constant approximation algorithm for locating the target in the set. We then extend our approach for scenarios where the constraints are defined in terms of general cost functions that depend only on the size of the query and provide an approximation algorithm that can find the target within O(log(log n)) gap from the cost of the optimum algorithm. Submodular functions come as a natural generalization of cost functions with decreasing marginals. Under submodular set constraints, we devise an approximation algorithm that can find the target within O(log n) gap from the cost of the optimum algorithm. The proposed algorithms are greedy in a sense that at each step they select a query that most evenly splits the set without violating the underlying constraints. These results can be applied to network tomography, active learning and interactive content search.
Cite as

Amin Karbasi and Morteza Zadimoghaddam. Constrained Binary Identification Problem. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 550-561, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{karbasi_et_al:LIPIcs.STACS.2013.550,
  author =	{Karbasi, Amin and Zadimoghaddam, Morteza},
  title =	{{Constrained Binary Identification Problem}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{550--561},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.550},
  URN =		{urn:nbn:de:0030-drops-39647},
  doi =		{10.4230/LIPIcs.STACS.2013.550},
  annote =	{Keywords: Network Tomography, Binary Identification Problem, Approximation Algorithms, Graph Algorithms, Tree Search Strategies, Entropy}
}
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