4 Search Results for "Karakostas, George"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.11
On Finding Randomly Planted Cliques in Arbitrary Graphs

Authors: Francesco Agrimonti, Marco Bressan, and Tommaso d'Orsi

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

Abstract
We study a planted clique model introduced by Feige [Uriel Feige, 2021] where a complete graph of size c⋅ n is planted uniformly at random in an arbitrary n-vertex graph. We give a simple deterministic algorithm that, in almost linear time, recovers a clique of size (c/3)^O(1/c) ⋅ n as long as the original graph has maximum degree at most (1-p)n for some fixed p > 0. The proof hinges on showing that the degrees of the final graph are correlated with the planted clique, in a way similar to (but more intricate than) the classical G(n,1/2)+K_√n planted clique model. Our algorithm suggests a separation from the worst-case model, where, assuming the Unique Games Conjecture, no polynomial algorithm can find cliques of size Ω(n) for every fixed c > 0, even if the input graph has maximum degree (1-p)n. Our techniques extend beyond the planted clique model. For example, when the planted graph is a balanced biclique, we recover a balanced biclique of size larger than the best guarantees known for the worst case.
Cite as

Francesco Agrimonti, Marco Bressan, and Tommaso d'Orsi. On Finding Randomly Planted Cliques in Arbitrary Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{agrimonti_et_al:LIPIcs.APPROX/RANDOM.2025.11,
  author =	{Agrimonti, Francesco and Bressan, Marco and d'Orsi, Tommaso},
  title =	{{On Finding Randomly Planted Cliques in Arbitrary Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{11:1--11:18},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-243774},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.11},
  annote =	{Keywords: Computational Complexity, Planted Clique, Semi-random, Unique Games Conjecture, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.28
Approximation Algorithms for the Generalized Point-To-Point Problem

Authors: Zachary Friggstad, Mohammad R. Salavatipour, and Hao Sun

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

Abstract
We consider the Generalized Point-to-Point (GP2P) problem in which we have an edge-weighted graph G with (possibly negative) node charges ϕ(v) ∈ ℤ. The goal is to find a minimum-cost set of edges such that each component has nonnegative total charge. Viewing the positive charges as specifying supply and negative charges as demand quantities at various nodes, the problem is equivalent to build the cheapest network so that it is possible to satisfy all demands by routing supplies across the network. This problem is a significant generalization of other network design problems such as the well-studied Steiner Forest problem. Even the special case of only having one single demand point (having charge -k and all the other nodes having charge +1) is capturing the k-Minimum Spanning Tree problem. Earlier work by Hajiaghayi et al. (2016) [Hajiaghayi et al., 2016] gave an O(log n) approximation in pseudo-polynomial time with further improved guarantees if the total supply is not much larger than the total demand, and also a 2-approximation if the total supply equals the total demand. Our contributions are four-fold: (a) we show how known k-Minimum Spanning Tree approximations can be extended to GP2P approximations while losing only a ε-factor if the number of demand points in the instance is bounded by a constant, (b) we improve the running time to be Fixed-Parameter Tractable (FPT) in the number of demand points in constant-dimensional Euclidean metrics, (c) we give a 2-approximation in instances where edge costs are all 1 and ϕ(v) = ± 1 for each node v and show such instances are APX-hard, and (d) we show how the logarithmic approximations in earlier work can be modified to run in truly polynomial time.
Cite as

Zachary Friggstad, Mohammad R. Salavatipour, and Hao Sun. Approximation Algorithms for the Generalized Point-To-Point Problem. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.28,
  author =	{Friggstad, Zachary and Salavatipour, Mohammad R. and Sun, Hao},
  title =	{{Approximation Algorithms for the Generalized Point-To-Point Problem}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{28:1--28:16},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-242599},
  doi =		{10.4230/LIPIcs.WADS.2025.28},
  annote =	{Keywords: Point-to-Point Network design, Approximation, Steiner Forest, k-MST}
}
Document
DOI: 10.4230/LIPIcs.WABI.2025.3
Approximability of Longest Run Subsequence and Complementary Minimization Problems

Authors: Yuichi Asahiro, Mingyang Gong, Jesper Jansson, Guohui Lin, Sichen Lu, Eiji Miyano, Hirotaka Ono, Toshiki Saitoh, and Shunichi Tanaka

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
We study the polynomial-time approximability of the Longest Run Subsequence problem (LRS for short) and its complementary minimization variant Minimum Run Subsequence Deletion problem (MRSD for short). For a string S = s₁ ⋯ s_n over an alphabet Σ, a subsequence S' of S is S' = s_{i₁} ⋯ s_{i_p}, such that 1 ≤ i₁ < i₂ < … < i_p ≤ |S|. A run of a symbol σ ∈ Σ in S is a maximal substring of consecutive occurrences of σ. A run subsequence S' of S is a subsequence of S in which every symbol σ ∈ Σ occurs in at most one run. The co-subsequence ̅{S'} of the subsequence S' = s_{i₁} ⋯ s_{i_p} in S is the subsequence obtained by deleting all the characters in S' from S, i.e., ̅{S'} = s_{j₁} ⋯ s_{j_{n-p}} such that j₁ < j₂ < … < j_{n-p} and {j₁, …, j_{n-p}} = {1, …, n}⧵ {i₁, …, i_p}. Given a string S, the goal of LRS (resp., MRSD) is to find a run subsequence S^* of S such that the length |S^*| is maximized (resp., the number | ̅{S^*}| of deleted symbols from S is minimized) over all the run subsequences of S. Let k be the maximum number of symbol occurrences in the input S. It is known that LRS and MRSD are APX-hard even if k = 2. In this paper, we show that LRS can be approximated in polynomial time within factors of (k+2)/3 for k = 2 or 3, and 2(k+1)/5 for every k ≥ 4. Furthermore, we show that MRSD can be approximated in linear time within a factor of (k+4)/4 if k is even and (k+3)/4 if k is odd.
Cite as

Yuichi Asahiro, Mingyang Gong, Jesper Jansson, Guohui Lin, Sichen Lu, Eiji Miyano, Hirotaka Ono, Toshiki Saitoh, and Shunichi Tanaka. Approximability of Longest Run Subsequence and Complementary Minimization Problems. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{asahiro_et_al:LIPIcs.WABI.2025.3,
  author =	{Asahiro, Yuichi and Gong, Mingyang and Jansson, Jesper and Lin, Guohui and Lu, Sichen and Miyano, Eiji and Ono, Hirotaka and Saitoh, Toshiki and Tanaka, Shunichi},
  title =	{{Approximability of Longest Run Subsequence and Complementary Minimization Problems}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.3},
  URN =		{urn:nbn:de:0030-drops-239290},
  doi =		{10.4230/LIPIcs.WABI.2025.3},
  annote =	{Keywords: Longest run subsequence, minimum run subsequence deletion, approximation algorithm}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.5
Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

Authors: George Karakostas and Stavros G. Kolliopoulos

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

Abstract
We study the classic weighted maximum throughput problem on unrelated machines. We give a (1-1/e-ε)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ-approximation algorithm for the single-machine problem to obtain an approximation factor of (1-1/e)ρ -ε for the corresponding unrelated-machines problem, for any ε > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1-1/e) -ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine.
Cite as

George Karakostas and Stavros G. Kolliopoulos. Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{karakostas_et_al:LIPIcs.APPROX/RANDOM.2023.5,
  author =	{Karakostas, George and Kolliopoulos, Stavros G.},
  title =	{{Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{5:1--5:17},
  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.2023.5},
  URN =		{urn:nbn:de:0030-drops-188305},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.5},
  annote =	{Keywords: scheduling, maximum weighted throughput, unrelated machines, approximation algorithm, PTAS}
}
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