4 Search Results for "Marcinkowski, Jan"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.15
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

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

Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.
Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.120
Caching Connections in Matchings

Authors: Yaniv Sadeh and Haim Kaplan

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

Abstract
Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a natural combinatorial structure and therefore may find additional applications in theory and practice. In the Caching in Matchings problem our cache consists of k matchings of connections between servers that form a bipartite graph. To cache a connection we insert it into one of the k matchings possibly evicting at most two other connections from this matching. This problem resembles the problem known as Connection Caching [Cohen et al., 2000], where we also cache connections but our only restriction is that they form a graph with bounded degree k. Our results show a somewhat surprising qualitative separation between the problems: The competitive ratio of any online algorithm for caching in matchings must depend on the size of the graph. Specifically, we give a deterministic O(nk) competitive and randomized O(n log k) competitive algorithms for caching in matchings, where n is the number of servers and k is the number of matchings. We also show that the competitive ratio of any deterministic algorithm is Ω(max(n/k,k)) and of any randomized algorithm is Ω(log (n/(k² log k)) ⋅ log k). In particular, the lower bound for randomized algorithms is Ω(log n) regardless of k, and can be as high as Ω(log² n) if k = n^{1/3}, for example. We also show that if we allow the algorithm to use at least 2k-1 matchings compared to k used by the optimum then we match the competitive ratios of connection catching which are independent of n. Interestingly, we also show that even a single extra matching for the algorithm allows to get substantially better bounds.
Cite as

Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120,
  author =	{Sadeh, Yaniv and Kaplan, Haim},
  title =	{{Caching Connections in Matchings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{120:1--120:20},
  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.2024.120},
  URN =		{urn:nbn:de:0030-drops-202639},
  doi =		{10.4230/LIPIcs.ICALP.2024.120},
  annote =	{Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.45
Online Facility Location with Linear Delay

Authors: Marcin Bienkowski, Martin Böhm, Jarosław Byrka, and Jan Marcinkowski

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
In the problem of online facility location with delay, a sequence of n clients appear in the metric space, and they need to be eventually connected to some open facility. The clients do not have to be connected immediately, but such a choice comes with a certain penalty: each client incurs a waiting cost (equal to the difference between its arrival and its connection time). At any point in time, an algorithm may decide to open a facility and connect any subset of clients to it. That is, an algorithm needs to balance three types of costs: cost of opening facilities, costs of connecting clients, and the waiting costs of clients. We study a natural variant of this problem, where clients may be connected also to an already open facility, but such action incurs an extra cost: an algorithm pays for waiting of the facility (a cost incurred separately for each such "late" connection). This is reminiscent of online matching with delays, where both sides of the connection incur a waiting cost. We call this variant two-sided delay to differentiate it from the previously studied one-sided delay, where clients may connect to a facility only at its opening time. We present an O(1)-competitive deterministic algorithm for the two-sided delay variant. Our approach is an extension of the approach used by Jain, Mahdian and Saberi [STOC 2002] for analyzing the performance of offline algorithms for facility location. To this end, we substantially simplify the part of the original argument in which a bound on the sequence of factor-revealing LPs is derived. We then show how to transform our O(1)-competitive algorithm for the two-sided delay variant to O(log n / log log n)-competitive deterministic algorithm for one-sided delays. This improves the known O(log n) bound by Azar and Touitou [FOCS 2020]. We note that all previous online algorithms for problems with delays in general metrics have at least logarithmic ratios.
Cite as

Marcin Bienkowski, Martin Böhm, Jarosław Byrka, and Jan Marcinkowski. Online Facility Location with Linear Delay. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bienkowski_et_al:LIPIcs.APPROX/RANDOM.2022.45,
  author =	{Bienkowski, Marcin and B\"{o}hm, Martin and Byrka, Jaros{\l}aw and Marcinkowski, Jan},
  title =	{{Online Facility Location with Linear Delay}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{45:1--45:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.45},
  URN =		{urn:nbn:de:0030-drops-171678},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.45},
  annote =	{Keywords: online facility location, network design problems, facility location with delay, JMS algorithm, competitive analysis, factor revealing LP}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.1
Constant-Factor FPT Approximation for Capacitated k-Median

Authors: Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski, Syed M. Meesum, and Michał Włodarczyk

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon.
Cite as

Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski, Syed M. Meesum, and Michał Włodarczyk. Constant-Factor FPT Approximation for Capacitated k-Median. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{adamczyk_et_al:LIPIcs.ESA.2019.1,
  author =	{Adamczyk, Marek and Byrka, Jaros{\l}aw and Marcinkowski, Jan and Meesum, Syed M. and W{\l}odarczyk, Micha{\l}},
  title =	{{Constant-Factor FPT Approximation for Capacitated k-Median}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.1},
  URN =		{urn:nbn:de:0030-drops-111225},
  doi =		{10.4230/LIPIcs.ESA.2019.1},
  annote =	{Keywords: K-median, Clustering, Approximation Algorithms, Fixed Parameter Tractability}
}
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