5 Search Results for "Avin, Chen"

Document
DOI: 10.4230/LIPIcs.AofA.2024.22
The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension

Authors: Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
It is celebrated that a simple random walk on ℤ and ℤ² returns to the initial vertex v infinitely many times during infinitely many transitions, which is said recurrent, while it returns to v only finite times on ℤ^d for d ≥ 3, which is said transient. It is also known that a simple random walk on a growing region on ℤ^d can be recurrent depending on growing speed for any fixed d. This paper shows that a simple random walk on {0,1,…,N}ⁿ with an increasing n and a fixed N can be recurrent depending on the increasing speed of n. Precisely, we are concerned with a specific model of a random walk on a growing graph (RWoGG) and show a phase transition between the recurrence and transience of the random walk regarding the growth speed of the graph. For the proof, we develop a pausing coupling argument introducing the notion of weakly less homesick as graph growing (weakly LHaGG).
Cite as

Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai. The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kumamoto_et_al:LIPIcs.AofA.2024.22,
  author =	{Kumamoto, Shuma and Kijima, Shuji and Shirai, Tomoyuki},
  title =	{{The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.22},
  URN =		{urn:nbn:de:0030-drops-204577},
  doi =		{10.4230/LIPIcs.AofA.2024.22},
  annote =	{Keywords: Random walk, dynamic graph, recurrence, transience, coupling}
}
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
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.35
Brief Announcement: On Self-Adjusting Skip List Networks

Authors: Chen Avin, Iosif Salem, and Stefan Schmid

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
This paper explores the design of dynamic network topologies which adjust to the workload they serve, in an online manner. Such self-adjusting networks (SANs) are enabled by emerging optical technologies, and can be found, e.g., in datacenters. SANs can be used to reduce routing costs by moving frequently communicating nodes topologically closer. This paper presents SANs which provide, for the first time, provable working set guarantees: the routing cost between node pairs is proportional to how recently these nodes communicated last time. Our SANs rely on skip lists (which serve as the topology) and provide additional interesting properties such as local routing.
Cite as

Chen Avin, Iosif Salem, and Stefan Schmid. Brief Announcement: On Self-Adjusting Skip List Networks. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 35:1-35:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{avin_et_al:LIPIcs.DISC.2019.35,
  author =	{Avin, Chen and Salem, Iosif and Schmid, Stefan},
  title =	{{Brief Announcement: On Self-Adjusting Skip List Networks}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{35:1--35:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.35},
  URN =		{urn:nbn:de:0030-drops-113423},
  doi =		{10.4230/LIPIcs.DISC.2019.35},
  annote =	{Keywords: self-adjusting networks, skip lists, working set, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.5
Demand-Aware Network Designs of Bounded Degree

Authors: Chen Avin, Kaushik Mondal, and Stefan Schmid

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
Traditionally, networks such as datacenter interconnects are designed to optimize worst-case performance under arbitrary traffic patterns. Such network designs can however be far from optimal when considering the actual workloads and traffic patterns which they serve. This insight led to the development of demand-aware datacenter interconnects which can be reconfigured depending on the workload. Motivated by these trends, this paper initiates the algorithmic study of demand-aware networks (DANs), and in particular the design of bounded-degree networks. The inputs to the network design problem are a discrete communication request distribution, D, defined over communicating pairs from the node set V, and a bound, d, on the maximum degree. In turn, our objective is to design an (undirected) demand-aware network N = (V,E) of bounded-degree d, which provides short routing paths between frequently communicating nodes distributed across N. In particular, the designed network should minimize the expected path length on N (with respect to D), which is a basic measure of the efficiency of the network. We show that this fundamental network design problem exhibits interesting connections to several classic combinatorial problems and to information theory. We derive a general lower bound based on the entropy of the communication pattern D, and present asymptotically optimal network-aware design algorithms for important distribution families, such as sparse distributions and distributions of locally bounded doubling dimensions.
Cite as

Chen Avin, Kaushik Mondal, and Stefan Schmid. Demand-Aware Network Designs of Bounded Degree. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{avin_et_al:LIPIcs.DISC.2017.5,
  author =	{Avin, Chen and Mondal, Kaushik and Schmid, Stefan},
  title =	{{Demand-Aware Network Designs of Bounded Degree}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.5},
  URN =		{urn:nbn:de:0030-drops-80153},
  doi =		{10.4230/LIPIcs.DISC.2017.5},
  annote =	{Keywords: Network design, reconfigurable networks, datacenter topology, peer-topeer computing, entropy, sparse spanners}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2017.58
Brief Announcement: Distributed SplayNets

Authors: Bruna S. Peres, Olga Goussevskaia, Stefan Schmid, and Chen Avin

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
SplayNets are reconfigurable networks which adjust to the communication pattern over time. We present DiSplayNets, a distributed (concurrent and decentralized) implementation of SplayNets.
Cite as

Bruna S. Peres, Olga Goussevskaia, Stefan Schmid, and Chen Avin. Brief Announcement: Distributed SplayNets. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 58:1-58:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{peres_et_al:LIPIcs.DISC.2017.58,
  author =	{Peres, Bruna S. and Goussevskaia, Olga and Schmid, Stefan and Avin, Chen},
  title =	{{Brief Announcement: Distributed SplayNets}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{58:1--58:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.58},
  URN =		{urn:nbn:de:0030-drops-79661},
  doi =		{10.4230/LIPIcs.DISC.2017.58},
  annote =	{Keywords: Decentralization, Concurrency, Reconfigurable Networks}
}
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