16 Search Results for "Duan, Ran"


Document
Streaming Matching and Edge Cover in Practice

Authors: S M Ferdous, Alex Pothen, and Mahantesh Halappanavar

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)


Abstract
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.

Cite as

S M Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming Matching and Edge Cover in Practice. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{ferdous_et_al:LIPIcs.SEA.2024.12,
  author =	{Ferdous, S M and Pothen, Alex and Halappanavar, Mahantesh},
  title =	{{Streaming Matching and Edge Cover in Practice}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.12},
  URN =		{urn:nbn:de:0030-drops-203773},
  doi =		{10.4230/LIPIcs.SEA.2024.12},
  annote =	{Keywords: Matching, Edge Cover, Semi-Streaming Algorithm, Parallel Algorithms, Algorithm Engineering}
}
Document
Track A: Algorithms, Complexity and Games
Faster Algorithms for Dual-Failure Replacement Paths

Authors: Shiri Chechik and Tianyi Zhang

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


Abstract
Given a simple weighted directed graph G = (V, E, ω) on n vertices as well as two designated terminals s, t ∈ V, our goal is to compute the shortest path from s to t avoiding any pair of presumably failed edges f₁, f₂ ∈ E, which is a natural generalization of the classical replacement path problem which considers single edge failures only. This dual failure replacement paths problem was recently studied by Vassilevska Williams, Woldeghebriel and Xu [FOCS 2022] who designed a cubic time algorithm for general weighted digraphs which is conditionally optimal; in the same paper, for unweighted graphs where ω ≡ 1, the authors presented an algebraic algorithm with runtime Õ(n^{2.9146}), as well as a conditional lower bound of n^{8/3-o(1)} against combinatorial algorithms. However, it was unknown in their work whether fast matrix multiplication is necessary for a subcubic runtime in unweighted digraphs. As our primary result, we present the first truly subcubic combinatorial algorithm for dual failure replacement paths in unweighted digraphs. Our runtime is Õ(n^{3-1/18}). Besides, we also study algebraic algorithms for digraphs with small integer edge weights from {-M, -M+1, ⋯, M-1, M}. As our secondary result, we obtained a runtime of Õ(Mn^{2.8716}), which is faster than the previous bound of Õ(M^{2/3}n^{2.9144} + Mn^{2.8716}) from [Vassilevska Williams, Woldeghebriela and Xu, 2022].

Cite as

Shiri Chechik and Tianyi Zhang. Faster Algorithms for Dual-Failure Replacement Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{chechik_et_al:LIPIcs.ICALP.2024.41,
  author =	{Chechik, Shiri and Zhang, Tianyi},
  title =	{{Faster Algorithms for Dual-Failure Replacement Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{41:1--41:20},
  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.2024.41},
  URN =		{urn:nbn:de:0030-drops-201849},
  doi =		{10.4230/LIPIcs.ICALP.2024.41},
  annote =	{Keywords: graph algorithms, shortest paths, replacement paths}
}
Document
Track A: Algorithms, Complexity and Games
Decremental Matching in General Weighted Graphs

Authors: Aditi Dudeja

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


Abstract
In this paper, we consider the problem of maintaining a (1-ε)-approximate maximum weight matching in a dynamic graph G, while the adversary makes changes to the edges of the graph. In the fully dynamic setting, where both edge insertions and deletions are allowed, Gupta and Peng [Manoj Gupta and Richard Peng, 2013] gave an algorithm for this problem with an update time of Õ_ε(√m). We study a natural relaxation of this problem, namely the decremental model, where the adversary is only allowed to delete edges. For the unweighted version of this problem in general (possibly, non-bipartite) graphs, [Sepehr Assadi et al., 2022] gave a decremental algorithm with update time O_ε(poly(log n)). However, beating Õ_ε(√m) update time remained an open problem for the weighted version in general graphs. In this paper, we bridge the gap between unweighted and weighted general graphs for the decremental setting. We give a O_ε(poly(log n)) update time algorithm that maintains a (1-ε) approximate maximum weight matching under adversarial deletions. Like the decremental algorithm of [Sepehr Assadi et al., 2022], our algorithm is randomized, but works against an adaptive adversary. It also matches the time bound for the unweighted version upto dependencies on ε and a log R factor, where R is the ratio between the maximum and minimum edge weight in G.

Cite as

Aditi Dudeja. Decremental Matching in General Weighted Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{dudeja:LIPIcs.ICALP.2024.59,
  author =	{Dudeja, Aditi},
  title =	{{Decremental Matching in General Weighted Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{59:1--59:20},
  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.2024.59},
  URN =		{urn:nbn:de:0030-drops-202020},
  doi =		{10.4230/LIPIcs.ICALP.2024.59},
  annote =	{Keywords: Weighted Matching, Dynamic Algorithms, Adaptive Adversary}
}
Document
Track A: Algorithms, Complexity and Games
Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity

Authors: Yaowei Long and Yunfan Wang

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


Abstract
We study the sensitivity oracles problem for subgraph connectivity in the decremental and fully dynamic settings. In the fully dynamic setting, we preprocess an n-vertices m-edges undirected graph G with n_{off} deactivated vertices initially and the others are activated. Then we receive a single update D ⊆ V(G) of size |D| = d ≤ d_{⋆}, representing vertices whose states will be switched. Finally, we get a sequence of queries, each of which asks the connectivity of two given vertices u and v in the activated subgraph. The decremental setting is a special case when there is no deactivated vertex initially, and it is also known as the vertex-failure connectivity oracles problem. We present a better deterministic vertex-failure connectivity oracle with Ô(d_{⋆}m) preprocessing time, Õ(m) space, Õ(d²) update time and O(d) query time, which improves the update time of the previous almost-optimal oracle [Long and Saranurak, 2022] from Ô(d²) to Õ(d²). We also present a better deterministic fully dynamic sensitivity oracle for subgraph connectivity with Ô(min{m(n_{off} + d_{⋆}),n^{ω}}) preprocessing time, Õ(min{m(n_{off} + d_{⋆}),n²}) space, Õ(d²) update time and O(d) query time, which significantly improves the update time of the state of the art [Bingbing Hu et al., 2023] from Õ(d⁴) to Õ(d²). Furthermore, our solution is even almost-optimal assuming popular fine-grained complexity conjectures.

Cite as

Yaowei Long and Yunfan Wang. Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 109:1-109:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{long_et_al:LIPIcs.ICALP.2024.109,
  author =	{Long, Yaowei and Wang, Yunfan},
  title =	{{Better Decremental and Fully Dynamic Sensitivity Oracles for Subgraph Connectivity}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{109:1--109:20},
  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.2024.109},
  URN =		{urn:nbn:de:0030-drops-202523},
  doi =		{10.4230/LIPIcs.ICALP.2024.109},
  annote =	{Keywords: connectivity, sensitivity}
}
Document
Track A: Algorithms, Complexity and Games
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)


Copy BibTex To Clipboard

@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
Track A: Algorithms, Complexity and Games
Faster Cut-Equivalent Trees in Simple Graphs

Authors: Tianyi Zhang

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
Let G = (V, E) be an undirected connected simple graph on n vertices. A cut-equivalent tree of G is an edge-weighted tree on the same vertex set V, such that for any pair of vertices s, t ∈ V, the minimum (s, t)-cut in the tree is also a minimum (s, t)-cut in G, and these two cuts have the same cut value. In a recent paper [Abboud, Krauthgamer and Trabelsi, STOC 2021], the authors propose the first subcubic time algorithm for constructing a cut-equivalent tree. More specifically, their algorithm has Õ(n^{2.5}) running time. Later on, this running time was significantly improved to n^{2+o(1)} by two independent works [Abboud, Krauthgamer and Trabelsi, FOCS 2021] and [Li, Panigrahi, Saranurak, FOCS 2021], and then to (m+n^{1.9})^{1+o(1)} by [Abboud, Krauthgamer and Trabelsi, SODA 2022]. In this paper, we improve the running time to Õ(n²) graphs if near-linear time max-flow algorithms exist, or Õ(n^{17/8}) using the currently fastest max-flow algorithm. Although our algorithm is slower than previous works, the runtime bound becomes better by a sub-polynomial factor in dense simple graphs when assuming near-linear time max-flow algorithms.

Cite as

Tianyi Zhang. Faster Cut-Equivalent Trees in Simple Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 109:1-109:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{zhang:LIPIcs.ICALP.2022.109,
  author =	{Zhang, Tianyi},
  title =	{{Faster Cut-Equivalent Trees in Simple Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{109:1--109:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.109},
  URN =		{urn:nbn:de:0030-drops-164507},
  doi =		{10.4230/LIPIcs.ICALP.2022.109},
  annote =	{Keywords: graph algorithms, minimum cuts, max-flow}
}
Document
Track A: Algorithms, Complexity and Games
Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time

Authors: Yong Gu and Hanlin Ren

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
We continue the study of distance sensitivity oracles (DSOs). Given a directed graph G with n vertices and edge weights in {1, 2, … , M}, we want to build a data structure such that given any source vertex u, any target vertex v, and any failure f (which is either a vertex or an edge), it outputs the length of the shortest path from u to v not going through f. Our main result is a DSO with preprocessing time O(n^2.5794 M) and constant query time. Previously, the best preprocessing time of DSOs for directed graphs is O(n^2.7233 M), and even in the easier case of undirected graphs, the best preprocessing time is O(n^2.6865 M) [Ren, ESA 2020]. One drawback of our DSOs, though, is that it only supports distance queries but not path queries. Our main technical ingredient is an algorithm that computes the inverse of a degree-d polynomial matrix (i.e. a matrix whose entries are degree-d univariate polynomials) modulo x^r. The algorithm is adapted from [Zhou, Labahn and Storjohann, Journal of Complexity, 2015], and we replace some of its intermediate steps with faster rectangular matrix multiplication algorithms. We also show how to compute unique shortest paths in a directed graph with edge weights in {1, 2, … , M}, in O(n^2.5286 M) time. This algorithm is crucial in the preprocessing algorithm of our DSO. Our solution improves the O(n^2.6865 M) time bound in [Ren, ESA 2020], and matches the current best time bound for computing all-pairs shortest paths.

Cite as

Yong Gu and Hanlin Ren. Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 76:1-76:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{gu_et_al:LIPIcs.ICALP.2021.76,
  author =	{Gu, Yong and Ren, Hanlin},
  title =	{{Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{76:1--76:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela 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.ICALP.2021.76},
  URN =		{urn:nbn:de:0030-drops-141450},
  doi =		{10.4230/LIPIcs.ICALP.2021.76},
  annote =	{Keywords: graph theory, shortest paths, distance sensitivity oracles}
}
Document
Track A: Algorithms, Complexity and Games
Deterministic Maximum Flows in Simple Graphs

Authors: Tianyi Zhang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
In this paper we are interested in deterministically computing maximum flows in undirected simple graphs where edges have unit capacities. When the input graph has n vertices and m edges, and the maximum flow is known to be upper bounded by τ as prior knowledge, our algorithm has running time Õ(m + n^{5/3}τ^{1/2}); in the extreme case where τ = Θ(n), our algorithm has running time Õ(n^{2.17}). This always improves upon the previous best deterministic upper bound Õ(n^{9/4}τ^{1/8}) by [Duan, 2013]. Furthermore, when τ ≥ n^{0.67} our algorithm is faster than a classical upper bound of O(m + nτ^{3/2}) by [Karger and Levin, 1998].

Cite as

Tianyi Zhang. Deterministic Maximum Flows in Simple Graphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 114:1-114:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{zhang:LIPIcs.ICALP.2021.114,
  author =	{Zhang, Tianyi},
  title =	{{Deterministic Maximum Flows in Simple Graphs}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{114:1--114:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela 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.ICALP.2021.114},
  URN =		{urn:nbn:de:0030-drops-141832},
  doi =		{10.4230/LIPIcs.ICALP.2021.114},
  annote =	{Keywords: graph algorithms, maximum flows, dynamic data structures}
}
Document
Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

Authors: Hanlin Ren

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph G = (V, E) with edge weights in {1, 2, … , M}, we need to preprocess it into a data structure, and answer the following queries: given vertices u,v,x ∈ V, output the length of the shortest path from u to v that does not go through x. Our main result is a simple DSO with Õ(n^2.7233 M²) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865 M²). Our algorithms are randomized with correct probability ≥ 1-1/n^c, for a constant c that can be made arbitrarily large. Previously, there is a DSO with Õ(n^2.8729 M) preprocessing time and polylog(n) query time [Chechik and Cohen, STOC'20]. At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time P and query time Q, then we can construct a DSO with preprocessing time P+Õ(Mn²)⋅ Q and query time O(1). (Here Õ(⋅) hides polylog(n) factors.)

Cite as

Hanlin Ren. Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{ren:LIPIcs.ESA.2020.79,
  author =	{Ren, Hanlin},
  title =	{{Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.79},
  URN =		{urn:nbn:de:0030-drops-129450},
  doi =		{10.4230/LIPIcs.ESA.2020.79},
  annote =	{Keywords: Graph theory, Failure-prone structures}
}
Document
Track A: Algorithms, Complexity and Games
Roundtrip Spanners with (2k-1) Stretch

Authors: Ruoxu Cen, Ran Duan, and Yong Gu

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)


Abstract
A roundtrip spanner of a directed graph G is a subgraph of G preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log (nW)) edges for every integer k > 1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log n) edges. While keeping the edge size small, our result improves the previous 2k+ε stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick'02; Zhu, Lam'18], and almost matches the undirected (2k-1)-spanner with O(n^(1+1/k)) edges [Althöfer et al. '93] when k is a constant, which is optimal under Erdös conjecture.

Cite as

Ruoxu Cen, Ran Duan, and Yong Gu. Roundtrip Spanners with (2k-1) Stretch. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 24:1-24:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{cen_et_al:LIPIcs.ICALP.2020.24,
  author =	{Cen, Ruoxu and Duan, Ran and Gu, Yong},
  title =	{{Roundtrip Spanners with (2k-1) Stretch}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{24:1--24:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.24},
  URN =		{urn:nbn:de:0030-drops-124313},
  doi =		{10.4230/LIPIcs.ICALP.2020.24},
  annote =	{Keywords: Graph theory, Deterministic algorithm, Roundtrip spanners}
}
Document
Track A: Algorithms, Complexity and Games
A Scaling Algorithm for Weighted f-Factors in General Graphs

Authors: Ran Duan, Haoqing He, and Tianyi Zhang

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)


Abstract
We study the maximum weight perfect f-factor problem on any general simple graph G = (V,E,ω) with positive integral edge weights w, and n = |V|, m = |E|. When we have a function f:V → ℕ_+ on vertices, a perfect f-factor is a generalized matching so that every vertex u is matched to exactly f(u) different edges. The previous best results on this problem have running time O(m f(V)) [Gabow 2018] or Õ(W(f(V))^2.373)) [Gabow and Sankowski 2013], where W is the maximum edge weight, and f(V) = ∑_{u ∈ V}f(u). In this paper, we present a scaling algorithm for this problem with running time Õ(mn^{2/3} log W). Previously this bound is only known for bipartite graphs [Gabow and Tarjan 1989]. The advantage is that the running time is independent of f(V), and consequently it breaks the Ω(mn) barrier for large f(V) even for the unweighted f-factor problem in general graphs.

Cite as

Ran Duan, Haoqing He, and Tianyi Zhang. A Scaling Algorithm for Weighted f-Factors in General Graphs. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{duan_et_al:LIPIcs.ICALP.2020.41,
  author =	{Duan, Ran and He, Haoqing and Zhang, Tianyi},
  title =	{{A Scaling Algorithm for Weighted f-Factors in General Graphs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.41},
  URN =		{urn:nbn:de:0030-drops-124487},
  doi =		{10.4230/LIPIcs.ICALP.2020.41},
  annote =	{Keywords: Scaling Algorithm, f-Factors, General Graphs}
}
Document
Track A: Algorithms, Complexity and Games
Faster Algorithms for All Pairs Non-Decreasing Paths Problem

Authors: Ran Duan, Ce Jin, and Hongxun Wu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time O~(n^{{3 + omega}/{2}}) = O~(n^{2.686}). Here n is the number of vertices, and omega < 2.373 is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for (max, min)-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for (max, min)-matrix product. The previous best upper bound for APNP on weighted digraphs was O~(n^{1/2(3 + {3 - omega}/{omega + 1} + omega)}) = O~(n^{2.78}) [Duan, Gu, Zhang 2018]. We also show an O~(n^2) time algorithm for APNP in undirected simple graphs which also reaches optimal within logarithmic factors.

Cite as

Ran Duan, Ce Jin, and Hongxun Wu. Faster Algorithms for All Pairs Non-Decreasing Paths Problem. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{duan_et_al:LIPIcs.ICALP.2019.48,
  author =	{Duan, Ran and Jin, Ce and Wu, Hongxun},
  title =	{{Faster Algorithms for All Pairs Non-Decreasing Paths Problem}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{48:1--48:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.48},
  URN =		{urn:nbn:de:0030-drops-106241},
  doi =		{10.4230/LIPIcs.ICALP.2019.48},
  annote =	{Keywords: graph optimization, matrix multiplication, non-decreasing paths}
}
Document
Approximating All-Pair Bounded-Leg Shortest Path and APSP-AF in Truly-Subcubic Time

Authors: Ran Duan and Hanlin Ren

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
In the bounded-leg shortest path (BLSP) problem, we are given a weighted graph G with nonnegative edge lengths, and we want to answer queries of the form "what's the shortest path from u to v, where only edges of length <=L are considered?". A more general problem is the APSP-AF (all-pair shortest path for all flows) problem, in which each edge has two weights - a length d and a capacity f, and a query asks about the shortest path from u to v where only edges of capacity >= f are considered. In this article we give an O~(n^{(omega+3)/2}epsilon^{-3/2}log W) time algorithm to compute a data structure that answers APSP-AF queries in O(log(epsilon^{-1}log (nW))) time and achieves (1+epsilon)-approximation, where omega < 2.373 is the exponent of time complexity of matrix multiplication, W is the upper bound of integer edge lengths, and n is the number of vertices. This is the first truly-subcubic time algorithm for these problems on dense graphs. Our algorithm utilizes the O(n^{(omega+3)/2}) time max-min product algorithm [Duan and Pettie 2009]. Since the all-pair bottleneck path (APBP) problem, which is equivalent to max-min product, can be seen as all-pair reachability for all flow, our approach indeed shows that these problems are almost equivalent in the approximation sense.

Cite as

Ran Duan and Hanlin Ren. Approximating All-Pair Bounded-Leg Shortest Path and APSP-AF in Truly-Subcubic Time. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 42:1-42:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{duan_et_al:LIPIcs.ICALP.2018.42,
  author =	{Duan, Ran and Ren, Hanlin},
  title =	{{Approximating All-Pair Bounded-Leg Shortest Path and APSP-AF in Truly-Subcubic Time}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{42:1--42:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.42},
  URN =		{urn:nbn:de:0030-drops-90467},
  doi =		{10.4230/LIPIcs.ICALP.2018.42},
  annote =	{Keywords: Graph Theory, Approximation Algorithms, Combinatorial Optimization}
}
Document
Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs

Authors: Ran Duan, Kaifeng Lyu, and Yuanhang Xie

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
In a directed graph G=(V,E) with a capacity on every edge, a bottleneck path (or widest path) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version of this problem in directed graphs, the previous best algorithm runs in O(m+n log n) (m=|E| and n=|V|) time, by Dijkstra search with Fibonacci heap [Fredman and Tarjan 1987]. We improve this time bound to O(m sqrt{log n}+sqrt{mn log n log log n}), which is O(n sqrt{log n log log n}) when m=O(n), thus it is the first algorithm which breaks the time bound of classic Fibonacci heap when m=o(n sqrt{log n}). It is a Las-Vegas randomized approach. By contrast, the s-t bottleneck path has algorithm with running time O(m beta(m,n)) [Chechik et al. 2016], where beta(m,n)=min{k >= 1: log^{(k)}n <= m/n}.

Cite as

Ran Duan, Kaifeng Lyu, and Yuanhang Xie. Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{duan_et_al:LIPIcs.ICALP.2018.43,
  author =	{Duan, Ran and Lyu, Kaifeng and Xie, Yuanhang},
  title =	{{Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.43},
  URN =		{urn:nbn:de:0030-drops-90475},
  doi =		{10.4230/LIPIcs.ICALP.2018.43},
  annote =	{Keywords: Graph Algorithm, Bottleneck Path, Combinatorial Optimization}
}
Document
Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs

Authors: Ran Duan, Yong Gu, and Le Zhang

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
We present improved algorithms for solving the All Pairs Non-decreasing Paths (APNP) problem on weighted digraphs. Currently, the best upper bound on APNP is O~(n^{(9+omega)/4})=O(n^{2.844}), obtained by Vassilevska Williams [TALG 2010 and SODA'08], where omega<2.373 is the usual exponent of matrix multiplication. Our first algorithm improves the time bound to O~(n^{2+omega/3})=O(n^{2.791}). The algorithm determines, for every pair of vertices s, t, the minimum last edge weight on a non-decreasing path from s to t, where a non-decreasing path is a path on which the edge weights form a non-decreasing sequence. The algorithm proposed uses the combinatorial properties of non-decreasing paths. Also a slightly improved algorithm with running time O(n^{2.78}) is presented.

Cite as

Ran Duan, Yong Gu, and Le Zhang. Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{duan_et_al:LIPIcs.ICALP.2018.44,
  author =	{Duan, Ran and Gu, Yong and Zhang, Le},
  title =	{{Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.44},
  URN =		{urn:nbn:de:0030-drops-90487},
  doi =		{10.4230/LIPIcs.ICALP.2018.44},
  annote =	{Keywords: Graph algorithms, Matrix multiplication, Non-decreasing paths}
}
  • Refine by Author
  • 7 Duan, Ran
  • 5 Zhang, Tianyi
  • 3 Gu, Yong
  • 3 Ren, Hanlin
  • 1 Cen, Ruoxu
  • Show More...

  • Refine by Classification
  • 6 Theory of computation → Design and analysis of algorithms
  • 3 Theory of computation → Shortest paths
  • 2 Theory of computation → Dynamic graph algorithms
  • 2 Theory of computation → Graph algorithms analysis
  • 1 Computing methodologies
  • Show More...

  • Refine by Keyword
  • 3 graph algorithms
  • 2 Combinatorial Optimization
  • 2 Graph theory
  • 2 shortest paths
  • 1 Adaptive Adversary
  • Show More...

  • Refine by Type
  • 16 document

  • Refine by Publication Year
  • 5 2024
  • 4 2018
  • 3 2020
  • 2 2021
  • 1 2019
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail