25 Search Results for "Shachnai, Hadas"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.50
On the PTAS Complexity of Multidimensional Knapsack

Authors: Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi

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

Abstract
We study the d-dimensional knapsack problem. We are given a set of items, each with a d-dimensional cost vector and a profit, along with a d-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A polynomial-time approximation scheme (PTAS) with running time n^{Θ(d/{ε})} has long been known for this problem, where {ε} is the error parameter and n is the encoding size. Despite decades of active research, the best running time of a PTAS has remained O(n^{⌈ d/{ε} ⌉ - d}). Unfortunately, existing lower bounds only cover the special case with two dimensions d = 2, and do not answer whether there is a n^{o(d/({ε)})}-time PTAS for larger values of d. In this work, we show that the running times of the best-known PTAS cannot be improved up to a polylogarithmic factor assuming the Exponential Time Hypothesis (ETH). Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions. Then, using a recent result of [Bafna Karthik and Minzer, STOC'25], we succeed in exhibiting tight trade-off between d and {ε} for all regimes of the parameters assuming d is sufficiently large. Informally, our result also shows that under ETH, for any function f there is no f(d/({ε)}) ⋅ n^{õ(d/({ε)})}-time (1-{ε})-approximation for d-dimensional knapsack, where n is the number of items and õ hides polylogarithmic factors in d/({ε)}.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi. On the PTAS Complexity of Multidimensional Knapsack. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{doronarad_et_al:LIPIcs.ITCS.2026.50,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Manurangsi, Pasin},
  title =	{{On the PTAS Complexity of Multidimensional Knapsack}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{50:1--50:22},
  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.2026.50},
  URN =		{urn:nbn:de:0030-drops-253377},
  doi =		{10.4230/LIPIcs.ITCS.2026.50},
  annote =	{Keywords: d-dimensional Knapsack, Multidimensional Knapsack, PTAS, CSP}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.58
One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts

Authors: Michal Feldman, Yoav Gal-Tzur, Tomasz Ponitka, and Maya Schlesinger

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

Abstract
We study multi-agent contract design with combinatorial actions, under budget constraints, and for a broad class of objective functions, including profit (principal’s utility), reward, and welfare. Our first result is a strong impossibility: For submodular reward functions, no randomized poly-time algorithm can approximate the optimal budget-feasible value within any finite factor, even with demand-oracle access. This result rules out extending known constant-factor guarantees from either (i) unbudgeted settings with combinatorial actions or (ii) budgeted settings with binary actions, to their combination. The hardness is tight: It holds even when all but one agent have binary actions and the remaining agent has just one additional action. On the positive side, we show that gross substitutes rewards (a well-studied strict subclass of submodular functions) admit a deterministic poly-time O(1)-approximation, using only value queries. Our results thus draw the first sharp separation between budgeted and unbudgeted settings in combinatorial contracts, and identifies gross substitutes as a tractable frontier for budgeted combinatorial contracts. Finally, we present an FPTAS for additive rewards, demonstrating that arbitrary approximation is tractable under any budget. This constitutes the first FPTAS for the multi-agent combinatorial-actions setting, even in the absence of budget constraints.
Cite as

Michal Feldman, Yoav Gal-Tzur, Tomasz Ponitka, and Maya Schlesinger. One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 58:1-58:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{feldman_et_al:LIPIcs.ITCS.2026.58,
  author =	{Feldman, Michal and Gal-Tzur, Yoav and Ponitka, Tomasz and Schlesinger, Maya},
  title =	{{One Action Too Many: Inapproximability of Budgeted Combinatorial Contracts}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{58:1--58:24},
  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.2026.58},
  URN =		{urn:nbn:de:0030-drops-253459},
  doi =		{10.4230/LIPIcs.ITCS.2026.58},
  annote =	{Keywords: Combinatorial Contracts, Algorithmic Contract Design, Budget-Feasible Contracts}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.23
Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection

Authors: Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo

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

Abstract
Payment channel networks (PCNs) are a promising technology that alleviates blockchain scalability by shifting the transaction load from the blockchain to the PCN. Nevertheless, the network topology has to be carefully designed to maximise the transaction throughput in PCNs. Additionally, users in PCNs also have to make optimal decisions on which transactions to forward and which to reject to prolong the lifetime of their channels. In this work, we consider an input sequence of transactions over p parties. Each transaction consists of a transaction size, source, and target, and can be either accepted or rejected (entailing a cost). The goal is to design a PCN topology among the p cooperating parties, along with the channel capacities, and then output a decision for each transaction in the sequence to minimise the cost of creating and augmenting channels, as well as the cost of rejecting transactions. Our main contribution is an 𝒪(p) approximation algorithm for the problem with p parties. We further show that with some assumptions on the distribution of transactions, we can reduce the approximation ratio to 𝒪(√p). We complement our theoretical analysis with an empirical study of our assumptions and approach in the context of the Lightning Network.
Cite as

Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo. Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chatterjee_et_al:LIPIcs.DISC.2025.23,
  author =	{Chatterjee, Krishnendu and K\v{r}i\v{s}\v{t}an, Jan Maty\'{a}\v{s} and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle},
  title =	{{Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{23:1--23:22},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-248402},
  doi =		{10.4230/LIPIcs.DISC.2025.23},
  annote =	{Keywords: Blockchains, Cryptocurrencies, Payment Channel Networks, Throughput, Optimisation, Graph Algorithms, Approximation 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}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.10
Improved Approximation Guarantees for Advertisement Placement

Authors: Waldo Gálvez, Roberto Oliva, and Victor Verdugo

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The advertisement placement problem involves selecting and scheduling ads within a timeline that has capacity constraints to maximize profit. Each task is characterized by its height, width, and profit, and must be fully scheduled across multiple time slots. This problem models practical scenarios such as internet advertising and energy management, and it also generalizes classical combinatorial optimization problems like the knapsack and bin packing problems. We present a simple (2+ε)-approximation algorithm for any ε > 0, which improves upon the state-of-the-art 3+ε factor established by Freund and Naor twenty years ago. Our approach combines rounding techniques with dynamic programming and an efficient extension of list scheduling. Furthermore, we enhance this method with linear programming techniques to provide an almost optimal (1+ε)-approximation algorithm under resource augmentation, which allows for a slight increase in time slot capacities.
Cite as

Waldo Gálvez, Roberto Oliva, and Victor Verdugo. Improved Approximation Guarantees for Advertisement Placement. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galvez_et_al:LIPIcs.APPROX/RANDOM.2025.10,
  author =	{G\'{a}lvez, Waldo and Oliva, Roberto and Verdugo, Victor},
  title =	{{Improved Approximation Guarantees for Advertisement Placement}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.10},
  URN =		{urn:nbn:de:0030-drops-243762},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.10},
  annote =	{Keywords: Advertisement Placement, Two-dimensional Packing, Geometric Knapsack, Resource Allocation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.18
q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations

Authors: Kiril Bangachev and S. Matthew Weinberg

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

Abstract
For a set M of m elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from 2^M to ℝ_{≥ 0}, parameterized by an integer q ∈ [2,m]. For a given q, we refer to the class as q-partitioning. A valuation function is subadditive if and only if it is 2-partitioning, and fractionally subadditive if and only if it is m-partitioning. Thus, our chain establishes an interpolation between subadditive and fractionally subadditive valuations. We show that this interpolation is smooth (q-partitioning valuations are "nearly" (q-1)-partitioning in a precise sense, Theorem 6), interpretable (the definition arises by analyzing the core of a cost-sharing game, à la the Bondareva-Shapley Theorem for fractionally subadditive valuations, Section 3.1), and non-trivial (the class of q-partitioning valuations is distinct for all q, Proposition 3). For domains where provable separations exist between subadditive and fractionally subadditive, we interpolate the stronger guarantees achievable for fractionally subadditive valuations to all q ∈ {2,…, m}. Two highlights are the following: 1) An Ω ((log log q)/(log log m))-competitive posted price mechanism for q-partitioning valuations. Note that this matches asymptotically the state-of-the-art for both subadditive (q = 2) [Paul Dütting et al., 2020], and fractionally subadditive (q = m) [Feldman et al., 2015]. 2) Two upper-tail concentration inequalities on 1-Lipschitz, q-partitioning valuations over independent items. One extends the state-of-the-art for q = m to q < m, the other improves the state-of-the-art for q = 2 for q > 2. Our concentration inequalities imply several corollaries that interpolate between subadditive and fractionally subadditive, for example: 𝔼[v(S)] ≤ (1 + 1/log q)Median[v(S)] + O(log q). To prove this, we develop a new isoperimetric inequality using Talagrand’s method of control by q points, which may be of independent interest. We also discuss other probabilistic inequalities and game-theoretic applications of q-partitioning valuations, and connections to subadditive MPH-k valuations [Tomer Ezra et al., 2019].
Cite as

Kiril Bangachev and S. Matthew Weinberg. q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bangachev_et_al:LIPIcs.ICALP.2025.18,
  author =	{Bangachev, Kiril and Weinberg, S. Matthew},
  title =	{{q-Partitioning Valuations: Exploring the Space Between Subadditive and Fractionally Subadditive Valuations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{18:1--18:20},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-233956},
  doi =		{10.4230/LIPIcs.ICALP.2025.18},
  annote =	{Keywords: Subadditive Functions, Fractionally Subadditive Functions, Posted Price Mechanisms, Concentration Inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.85
Towards the Proximity Conjecture on Group-Labeled Matroids

Authors: Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi

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

Abstract
Consider a matroid M whose ground set is equipped with a labeling to an abelian group. A basis of M is called F-avoiding if the sum of the labels of its elements is not in a forbidden label set F. Hörsch, Imolay, Mizutani, Oki, and Schwarcz (2024) conjectured that if an F-avoiding basis exists, then any basis can be transformed into an F-avoiding basis by exchanging at most |F| elements. This proximity conjecture is known to hold for certain specific groups; in the case where |F| ≤ 2; or when the matroid is subsequence-interchangeably base orderable (SIBO), which is a weakening of the so-called strongly base orderable (SBO) property. In this paper, we settle the proximity conjecture for sparse paving matroids or in the case where |F| ≤ 4. Related to the latter result, we present the first known example of a non-SIBO matroid. We further address the setting of multiple group-label constraints, showing proximity results for the cases of two labelings, SIBO matroids, matroids representable over a fixed, finite field, and sparse paving matroids.
Cite as

Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi. Towards the Proximity Conjecture on Group-Labeled Matroids. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garamvolgyi_et_al:LIPIcs.ICALP.2025.85,
  author =	{Garamv\"{o}lgyi, D\'{a}niel and Mizutani, Ryuhei and Oki, Taihei and Schwarcz, Tam\'{a}s and Yamaguchi, Yutaro},
  title =	{{Towards the Proximity Conjecture on Group-Labeled Matroids}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{85:1--85:17},
  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.2025.85},
  URN =		{urn:nbn:de:0030-drops-234628},
  doi =		{10.4230/LIPIcs.ICALP.2025.85},
  annote =	{Keywords: sparse paving matroid, subsequence-interchangeable base orderability, congruency constraint, multiple labelings}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.39
Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems

Authors: Barış Can Esmer and Ariel Kulik

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

Abstract
In this paper, we present Sampling with a Black Box, a unified framework for the design of parameterized approximation algorithms for vertex deletion problems (e.g., Vertex Cover, Feedback Vertex Set, etc.). The framework relies on two components: - A Sampling Step. A polynomial-time randomized algorithm that, given a graph G, returns a random vertex v such that the optimum of G⧵ {v} is smaller by 1 than the optimum of G, with some prescribed probability q. We show that such algorithms exist for multiple vertex deletion problems. - A Black Box algorithm which is either an exact parameterized algorithm, a polynomial-time approximation algorithm, or a parameterized-approximation algorithm. The framework combines these two components together. The sampling step is applied iteratively to remove vertices from the input graph, and then the solution is extended using the black box algorithm. The process is repeated sufficiently many times so that the target approximation ratio is attained with a constant probability. We use the technique to derive parameterized approximation algorithms for several vertex deletion problems, including Feedback Vertex Set, d-Hitting Set and 𝓁-Path Vertex Cover. In particular, for every approximation ratio 1 < β < 2, we attain a parameterized β-approximation for Feedback Vertex Set, which is faster than the parameterized β-approximation of [Jana, Lokshtanov, Mandal, Rai and Saurabh, MFCS 23']. Furthermore, our algorithms are always faster than the algorithms attained using Fidelity Preserving Transformations [Fellows, Kulik, Rosamond, and Shachnai, JCSS 18'].
Cite as

Barış Can Esmer and Ariel Kulik. Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canesmer_et_al:LIPIcs.ICALP.2025.39,
  author =	{Can Esmer, Bar{\i}\c{s} and Kulik, Ariel},
  title =	{{Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-234165},
  doi =		{10.4230/LIPIcs.ICALP.2025.39},
  annote =	{Keywords: Parameterized Approximation Algorithms, Random Sampling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.41
Residue Domination in Bounded-Treewidth Graphs

Authors: Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz

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

Abstract
For the vertex selection problem (σ,ρ)-DomSet one is given two fixed sets σ and ρ of integers and the task is to decide whether we can select vertices of the input graph such that, for every selected vertex, the number of selected neighbors is in σ and, for every unselected vertex, the number of selected neighbors is in ρ [Telle, Nord. J. Comp. 1994]. This framework covers many fundamental graph problems such as Independent Set and Dominating Set. We significantly extend the recent result by Focke et al. [SODA 2023] to investigate the case when σ and ρ are two (potentially different) residue classes modulo m ≥ 2. We study the problem parameterized by treewidth and present an algorithm that solves in time m^tw ⋅ n^O(1) the decision, minimization and maximization version of the problem. This significantly improves upon the known algorithms where for the case m ≥ 3 not even an explicit running time is known. We complement our algorithm by providing matching lower bounds which state that there is no (m-ε)^pw ⋅ n^O(1)-time algorithm parameterized by pathwidth pw, unless SETH fails. For m = 2, we extend these bounds to the minimization version as the decision version is efficiently solvable.
Cite as

Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz. Residue Domination in Bounded-Treewidth Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{greilhuber_et_al:LIPIcs.STACS.2025.41,
  author =	{Greilhuber, Jakob and Schepper, Philipp and Wellnitz, Philip},
  title =	{{Residue Domination in Bounded-Treewidth Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{41:1--41:20},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-228675},
  doi =		{10.4230/LIPIcs.STACS.2025.41},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Generalized Dominating Set, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.51
Parameterized Geometric Graph Modification with Disk Scaling

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

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

Abstract
The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph G and an integer k ∈ ℕ as input, the goal is to determine whether we can perform at most k operations on G to transform it into a graph belonging to a specified graph class ℱ. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized Geometric Graph Modification with Disk Scaling. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ITCS.2025.51,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Parameterized Geometric Graph Modification with Disk Scaling}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{51:1--51:17},
  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.2025.51},
  URN =		{urn:nbn:de:0030-drops-226795},
  doi =		{10.4230/LIPIcs.ITCS.2025.51},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.27
An EPTAS for Cardinality Constrained Multiple Knapsack via Iterative Randomized Rounding

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
In [Math. Oper. Res., 2011], Fleischer et al. introduced a powerful technique for solving the generic class of separable assignment problems (SAP), in which a set of items of given values and weights needs to be packed into a set of bins subject to separable assignment constraints, so as to maximize the total value. The approach of Fleischer at al. relies on solving a configuration LP and sampling a configuration for each bin independently based on the LP solution. While there is a SAP variant for which this approach yields the best possible approximation ratio, for various special cases, there are discrepancies between the approximation ratios obtained using the above approach and the state-of-the-art approximations. This raises the following natural question: Can we do better by iteratively solving the configuration LP and sampling a few bins at a time? To assess the potential of the iterative approach we consider a specific SAP variant as a case-study, Uniform Cardinality Constrained Multiple Knapsack, for which we answer this question affirmatively. The input is a set of items, each has a value and a weight, and a set of uniform capacity bins. The goal is to assign a subset of the items of maximum total value to the bins such that (i) the capacity of any bin is not exceeded, and (ii) the number of items assigned to each bin satisfies a given cardinality constraint. While the technique of Fleischer et al. yields a (1-1/e)-approximation for the problem, we show that iterative randomized rounding leads to efficient polynomial time approximation scheme (EPTAS), thus essentially resolving the complexity status of the problem. Our analysis of iterative randomized rounding may be useful for solving other SAP variants.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. An EPTAS for Cardinality Constrained Multiple Knapsack via Iterative Randomized Rounding. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doronarad_et_al:LIPIcs.APPROX/RANDOM.2024.27,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{An EPTAS for Cardinality Constrained Multiple Knapsack via Iterative Randomized Rounding}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.27},
  URN =		{urn:nbn:de:0030-drops-210204},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.27},
  annote =	{Keywords: multiple knapsack, cardinality constraint, EPTAS, iterative randomized rounding}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.56
Lower Bounds for Matroid Optimization Problems with a Linear Constraint

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study a family of matroid optimization problems with a linear constraint (MOL). In these problems, we seek a subset of elements which optimizes (i.e., maximizes or minimizes) a linear objective function subject to (i) a matroid independent set, or a matroid basis constraint, (ii) additional linear constraint. A notable member in this family is budgeted matroid independent set (BM), which can be viewed as classic 0/1-Knapsack with a matroid constraint. While special cases of BM, such as knapsack with cardinality constraint and multiple-choice knapsack, admit a fully polynomial-time approximation scheme (Fully PTAS), the best known result for BM on a general matroid is an Efficient PTAS. Prior to this work, the existence of a Fully PTAS for BM, and more generally, for any problem in the family of MOL problems, has been open. In this paper, we answer this question negatively by showing that none of the (non-trivial) problems in this family admits a Fully PTAS. This resolves the complexity status of several well studied problems. Our main result is obtained by showing first that exact weight matroid basis (EMB) does not admit a pseudo-polynomial time algorithm. This distinguishes EMB from the special cases of k-subset sum and EMB on a linear matroid, which are solvable in pseudo-polynomial time. We then obtain unconditional hardness results for the family of MOL problems in the oracle model (even if randomization is allowed), and show that the same results hold when the matroids are encoded as part of the input, assuming P ≠ NP. For the hardness proof of EMB, we introduce the Π-matroid family. This intricate subclass of matroids, which exploits the interaction between a weight function and the matroid constraint, may find use in tackling other matroid optimization problems.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. Lower Bounds for Matroid Optimization Problems with a Linear Constraint. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doronarad_et_al:LIPIcs.ICALP.2024.56,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Lower Bounds for Matroid Optimization Problems with a Linear Constraint}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{56:1--56:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.56},
  URN =		{urn:nbn:de:0030-drops-201990},
  doi =		{10.4230/LIPIcs.ICALP.2024.56},
  annote =	{Keywords: matroid optimization, budgeted problems, knapsack, approximation schemes}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.13
Budgeted Matroid Maximization: a Parameterized Viewpoint

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an 𝓁-matchoid ℳ on a ground set E, a profit function p:E → ℝ_{≥ 0}, a cost function c:E → ℝ_{≥ 0}, and a budget B ∈ ℝ_{≥ 0}, the goal is to find in the 𝓁-matchoid a feasible set S of maximum profit p(S) subject to the budget constraint, i.e., c(S) ≤ B. The budgeted 𝓁-matchoid (BM) problem includes as special cases budgeted 𝓁-dimensional matching and budgeted 𝓁-matroid intersection. A strong motivation for studying BM from parameterized viewpoint comes from the APX-hardness of unbudgeted 𝓁-dimensional matching (i.e., B = ∞) already for 𝓁 = 3. Nevertheless, while there are known FPT algorithms for the unbudgeted variants of the above problems, the budgeted variants are studied here for the first time through the lens of parameterized complexity. We show that BM parametrized by solution size is W[1]-hard, already with a degenerate single matroid constraint. Thus, an exact parameterized algorithm is unlikely to exist, motivating the study of FPT-approximation schemes (FPAS). Our main result is an FPAS for BM (implying an FPAS for 𝓁-dimensional matching and budgeted 𝓁-matroid intersection), relying on the notion of representative set - a small cardinality subset of elements which preserves the optimum up to a small factor. We also give a lower bound on the minimum possible size of a representative set which can be computed in polynomial time.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. Budgeted Matroid Maximization: a Parameterized Viewpoint. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{doronarad_et_al:LIPIcs.IPEC.2023.13,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Budgeted Matroid Maximization: a Parameterized Viewpoint}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.13},
  URN =		{urn:nbn:de:0030-drops-194329},
  doi =		{10.4230/LIPIcs.IPEC.2023.13},
  annote =	{Keywords: budgeted matching, budgeted matroid intersection, knapsack problems, FPT-approximation scheme}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.20
Improved Approximation for Two-Dimensional Vector Multiple Knapsack

Authors: Tomer Cohen, Ariel Kulik, and Hadas Shachnai

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We study the uniform 2-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated with a 2-dimensional weight vector and a positive profit, along with m 2-dimensional bins of uniform (unit) capacity in each dimension. The goal is to find an assignment of a subset of the items to the bins, such that the total weight of items assigned to a single bin is at most one in each dimension, and the total profit is maximized. Our main result is a (1 - (ln 2)/2 - ε)-approximation algorithm for 2VMK, for every fixed ε > 0, thus improving the best known ratio of (1 - 1/e - ε) which follows as a special case from a result of [Fleischer at al., MOR 2011]. Our algorithm relies on an adaptation of the Round&Approx framework of [Bansal et al., SICOMP 2010], originally designed for set covering problems, to maximization problems. The algorithm uses randomized rounding of a configuration-LP solution to assign items to ≈ m⋅ln 2 ≈ 0.693⋅m of the bins, followed by a reduction to the (1-dimensional) Multiple Knapsack problem for assigning items to the remaining bins.
Cite as

Tomer Cohen, Ariel Kulik, and Hadas Shachnai. Improved Approximation for Two-Dimensional Vector Multiple Knapsack. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.ISAAC.2023.20,
  author =	{Cohen, Tomer and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Improved Approximation for Two-Dimensional Vector Multiple Knapsack}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.20},
  URN =		{urn:nbn:de:0030-drops-193229},
  doi =		{10.4230/LIPIcs.ISAAC.2023.20},
  annote =	{Keywords: vector multiple knapsack, two-dimensional packing, randomized rounding, approximation algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.22
An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding

Authors: Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai

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

Abstract
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0,1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes, in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai. An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{doronarad_et_al:LIPIcs.APPROX/RANDOM.2023.22,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Shachnai, Hadas},
  title =	{{An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.22},
  URN =		{urn:nbn:de:0030-drops-188470},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.22},
  annote =	{Keywords: bin packing, partition-matroid, AFPTAS, LP-rounding}
}
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