Search Results

Documents authored by Pagourtzis, Aris

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.44
Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio

Authors: Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The Subset Sum Ratio problem (SSR) asks, given a multiset A of positive integers, to find two disjoint subsets of A such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the k-version of SSR, namely k-Subset Sum Ratio (k-SSR), which asks to minimize the largest-to-smallest ratio of sums of k disjoint subsets of A. We develop an approximation scheme for k-SSR running in O(n^{2k}/ε^{k-1}) time, where n = |A| and ε is the error parameter. To the best of our knowledge, this is the first FPTAS for k-SSR for fixed k > 2. We also study the k-way Number Partitioning Ratio (k-PART) problem, which differs from k-SSR in that the k subsets must constitute a partition of A; this problem in fact corresponds to the objective of minimizing the largest-to-smallest sum ratio in the family of Multiway Number Partitioning problems. We present a more involved FPTAS for k-PART, also achieving O(n^{2k}/ε^{k-1}) time complexity. Notably, k-PART is also equivalent to the Minimum Envy-Ratio problem with identical valuation functions, which has been studied in the context of fair division of indivisible goods. Thus, for the case of identical valuations, our FPTAS represents a significant improvement over the O(n^{4k²+1}/ε^{2k²}) bound obtained by Nguyen and Rothe’s FPTAS [Trung Thanh Nguyen and Jörg Rothe, 2014] for Minimum Envy-Ratio with general additive valuations. Lastly, we propose a second FPTAS for k-SSR, which employs carefully designed calls to the first one; the new scheme has a time complexity of Õ(n/ε^{3k-1}), thus being much faster when n≫ 1/ ε.
Cite as

Sotiris Kanellopoulos, Giorgos Mitropoulos, Antonis Antonopoulos, Nikos Leonardos, Aris Pagourtzis, Christos Pergaminelis, Stavros Petsalakis, and Kanellos Tsitouras. Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kanellopoulos_et_al:LIPIcs.ISAAC.2025.44,
  author =	{Kanellopoulos, Sotiris and Mitropoulos, Giorgos and Antonopoulos, Antonis and Leonardos, Nikos and Pagourtzis, Aris and Pergaminelis, Christos and Petsalakis, Stavros and Tsitouras, Kanellos},
  title =	{{Approximation Schemes for k-Subset Sum Ratio and k-Way Number Partitioning Ratio}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{44:1--44:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.44},
  URN =		{urn:nbn:de:0030-drops-249521},
  doi =		{10.4230/LIPIcs.ISAAC.2025.44},
  annote =	{Keywords: Fully polynomial-time approximation schemes, Subset Sum Ratio, Number Partitioning, Fair division, Envy minimization, Pseudo-polynomial time algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.80
Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks

Authors: Aris Pagourtzis and Tomasz Radzik

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We consider the classical broadcast problem in ad-hoc (that is, unknown topology) directed radio networks with no collision detection, under the additional assumption that at most h transmissions (shots) are available per node. We focus on adaptive deterministic protocols for small values of h. We provide asymptotically matching lower and upper bounds for the cases h=2 and h=3. While for h=2 our bound is quadratic, similar to the bound obtained for oblivious protocols, for h=3 we prove a sub-quadratic bound of Theta(n^2 log log n / log n), where n is the number of nodes in the network. The latter is the first result showing an adaptive algorithm which is asymptotically faster than oblivious h-shot broadcast protocols, for which a tight quadratic bound is known for every constant h. Our upper bound for h=3 is constructive, making use of constructions of graphs with large girth. We also show an improved upper bound of O(n^(1+alpha/sqrt{h})) for h >= 4, where alpha is an absolute constant independent of h. Our upper bound for h >= 4 is non-constructive.
Cite as

Aris Pagourtzis and Tomasz Radzik. Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 80:1-80:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{pagourtzis_et_al:LIPIcs.MFCS.2018.80,
  author =	{Pagourtzis, Aris and Radzik, Tomasz},
  title =	{{Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{80:1--80:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.80},
  URN =		{urn:nbn:de:0030-drops-96629},
  doi =		{10.4230/LIPIcs.MFCS.2018.80},
  annote =	{Keywords: Ad-hoc radio networks, wireless networks, deterministic broadcast, adaptive protocols, limited transmissions}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2006.684
Periodic Metro Scheduling

Authors: Evangelos Bampas, Georgia Kaouri, Michael Lampis, and Aris Pagourtzis

Published in: OASIcs, Volume 5, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06) (2006)

Abstract
We introduce the { extsc{Periodic Metro Sched-ul-ing}} ({ extsc{PMS}}) problem, which aims in generating a periodic timetable for a given set of routes and a given time period, in such a way that the minimum time distance between any two successive trains that pass from the same point of the network is maximized. This can be particularly useful in cases where trains use the same rail segment quite often, as happens in metropolitan rail networks. We present exact algorithms for ({ extsc{PMS}}) in chain and spider networks, and constant ratio approximation algorithms for ring networks and for a special class of tree networks. Some of our algorithms are based on a reduction to the { extsc{Path Coloring}} problem, while others rely on techniques specially designed for the new problem.
Cite as

Evangelos Bampas, Georgia Kaouri, Michael Lampis, and Aris Pagourtzis. Periodic Metro Scheduling. In 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06). Open Access Series in Informatics (OASIcs), Volume 5, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

Copy BibTex To Clipboard

@InProceedings{bampas_et_al:OASIcs.ATMOS.2006.684,
  author =	{Bampas, Evangelos and Kaouri, Georgia and Lampis, Michael and Pagourtzis, Aris},
  title =	{{Periodic Metro Scheduling}},
  booktitle =	{6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06)},
  pages =	{1--15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-01-9},
  ISSN =	{2190-6807},
  year =	{2006},
  volume =	{5},
  editor =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2006.684},
  URN =		{urn:nbn:de:0030-drops-6841},
  doi =		{10.4230/OASIcs.ATMOS.2006.684},
  annote =	{Keywords: Train scheduling, path coloring, delay-tolerant scheduling, periodic timetabling}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact