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Documents authored by Chakraborty, Sankardeep

Document
DOI: 10.4230/LIPIcs.ISAAC.2024.17
Succinct Data Structures for Baxter Permutation and Related Families

Authors: Sankardeep Chakraborty, Seungbum Jo, Geunho Kim, and Kunihiko Sadakane

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
A permutation π: [n] → [n] is a Baxter permutation if and only if it does not contain either of the patterns 2-41-3 and 3-14-2. Baxter permutations are one of the most widely studied subclasses of general permutation due to their connections with various combinatorial objects such as plane bipolar orientations and mosaic floorplans, etc. In this paper, we introduce a novel succinct representation (i.e., using o(n) additional bits from their information-theoretical lower bounds) for Baxter permutations of size n that supports π(i) and π^{-1}(j) queries for any i ∈ [n] in O(f₁(n)) and O(f₂(n)) time, respectively. Here, f₁(n) and f₂(n) are arbitrary increasing functions that satisfy the conditions ω(log n) and ω(log² n), respectively. This stands out as the first succinct representation with sub-linear worst-case query times for Baxter permutations. The main idea is to traverse the Cartesian tree on the permutation using a simple yet elegant two-stack algorithm which traverses the nodes in ascending order of their corresponding labels and stores the necessary information throughout the algorithm. Additionally, we consider a subclass of Baxter permutations called separable permutations, which do not contain either of the patterns 2-4-1-3 and 3-1-4-2. In this paper, we provide the first succinct representation of the separable permutation ρ: [n] → [n] of size n that supports both ρ(i) and ρ^{-1}(j) queries in O(1) time. In particular, this result circumvents Golynski’s [SODA 2009] lower bound result for trade-offs between redundancy and ρ(i) and ρ^{-1}(j) queries. Moreover, as applications of these permutations with the queries, we also introduce the first succinct representations for mosaic/slicing floorplans, and plane bipolar orientations, which can further support specific navigational queries on them efficiently.
Cite as

Sankardeep Chakraborty, Seungbum Jo, Geunho Kim, and Kunihiko Sadakane. Succinct Data Structures for Baxter Permutation and Related Families. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2024.17,
  author =	{Chakraborty, Sankardeep and Jo, Seungbum and Kim, Geunho and Sadakane, Kunihiko},
  title =	{{Succinct Data Structures for Baxter Permutation and Related Families}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.17},
  URN =		{urn:nbn:de:0030-drops-221441},
  doi =		{10.4230/LIPIcs.ISAAC.2024.17},
  annote =	{Keywords: Succinct data structure, Baxter permutation, Mosaic floorplan, Plane bipolar orientation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.18
Enhancing Generalized Compressed Suffix Trees, with Applications

Authors: Sankardeep Chakraborty, Kunihiko Sadakane, and Wiktor Zuba

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
Generalized suffix trees are data structures for storing and searching a set of strings. Though many string problems can be solved efficiently using them, their space usage can be large relative to the size of the input strings. For a set of strings with n characters in total, generalized suffix trees use O(n log n) bit space, which is much larger than the strings that occupy n log σ bits where σ is the alphabet size. Generalized compressed suffix trees use just O(n log σ) bits but support the same basic operations as the generalized suffix trees. However, for some sophisticated operations we need to add auxiliary data structures of O(n log n) bits. This becomes a bottleneck for applications involving big data. In this paper, we enhance the generalized compressed suffix trees while still retaining their space efficiency. First, we give an auxiliary data structure of O(n) bits for generalized compressed suffix trees such that given a suffix s of a string and another string t, we can find the suffix of t that is closest to s. Next, we give a o(n) bit data structure for finding the ancestor of a node in a (generalized) compressed suffix tree with given string depth. Finally, we give data structures for a generalization of the document listing problem from arrays to trees. We also show their applications to suffix-prefix matching problems.
Cite as

Sankardeep Chakraborty, Kunihiko Sadakane, and Wiktor Zuba. Enhancing Generalized Compressed Suffix Trees, with Applications. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2024.18,
  author =	{Chakraborty, Sankardeep and Sadakane, Kunihiko and Zuba, Wiktor},
  title =	{{Enhancing Generalized Compressed Suffix Trees, with Applications}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.18},
  URN =		{urn:nbn:de:0030-drops-221453},
  doi =		{10.4230/LIPIcs.ISAAC.2024.18},
  annote =	{Keywords: suffix tree, compact data structure, suffix-prefix query, weighted level ancestor}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.64
A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs

Authors: Kou Hamada, Sankardeep Chakraborty, Seungbum Jo, Takuto Koriyama, Kunihiko Sadakane, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Tree covering is a technique for decomposing a tree into smaller sized trees with desirable properties, and has been employed in various succinct data structures. However, significant hurdles stand in the way of a practical implementation of tree covering: a lot of pointers are used to maintain the tree-covering hierarchy and many indices for tree navigational queries consume theoretically negligible yet practically vast space. To tackle these problems, we propose a simple representation of tree covering using a balanced-parenthesis representation. The key to the proposal is the observation that every micro tree splits into at most two intervals on the BP representation. Utilizing the representation, we propose several data structures that represent a tree and its tree cover, which consequently allow micro tree compression with arbitrary coding and efficient tree navigational queries. We also applied our data structure to average-case optimal RMQ by Munro et al. [ESA 2021] and implemented the RMQ data structure. Our RMQ data structures spend less than 2n bits and process queries in a practical time on several settings of the performance evaluation, reducing the gap between theoretical space complexity and actual space consumption. For example, our implementation consumes 1.822n bits and processes queries in 5µs on average for random queries and in 13µs on average for the worst query widths. We also implement tree navigational operations while using the same amount of space as the RMQ data structures. We believe the representation can be widely utilized for designing practically memory-efficient data structures based on tree covering.
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Kou Hamada, Sankardeep Chakraborty, Seungbum Jo, Takuto Koriyama, Kunihiko Sadakane, and Srinivasa Rao Satti. A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 64:1-64:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hamada_et_al:LIPIcs.ESA.2024.64,
  author =	{Hamada, Kou and Chakraborty, Sankardeep and Jo, Seungbum and Koriyama, Takuto and Sadakane, Kunihiko and Satti, Srinivasa Rao},
  title =	{{A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{64:1--64:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.64},
  URN =		{urn:nbn:de:0030-drops-211359},
  doi =		{10.4230/LIPIcs.ESA.2024.64},
  annote =	{Keywords: Hypersuccinct trees, Succinct data structures, Range minimum queries, Binary trees}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.4
Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage

Authors: Girish Balakrishnan, Sankardeep Chakraborty, N. S. Narayanaswamy, and Kunihiko Sadakane

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
Chordal graphs is a well-studied large graph class that is also a strict super-class of path graphs. Munro and Wu (ISAAC 2018) have given an (n²/4+o(n²))-bit succinct representation for n-vertex unlabeled chordal graphs. A chordal graph G = (V,E) is the intersection graph of sub-trees of a tree T. Based on this characterization, the two parameters of chordal graphs which we consider in this work are leafage, introduced by Lin, McKee and West (Discussiones Mathematicae Graph Theory 1998) and vertex leafage, introduced by Chaplick and Stacho (Discret. Appl. Math. 2014). Leafage is the minimum number of leaves in any possible tree T characterizing G. Let L(u) denote the number of leaves of the sub-tree in T corresponding to u ∈ V and k = max_{u ∈ V} L(u). The smallest k for which there exists a tree T for G is called its vertex leafage. In this work, we improve the worst-case information theoretic lower bound of Munro and Wu (ISAAC 2018) for n-vertex unlabeled chordal graphs when vertex leafage is bounded and leafage is unbounded. The class of unlabeled k-vertex leafage chordal graphs that consists of all chordal graphs with vertex leafage at most k and unbounded leafage, denoted 𝒢_k, is introduced for the first time. For k > 0 in o(n^c), c > 0, we obtain a lower bound of ((k-1)n log n -kn log k - O(log n))-bits on the size of any data structure that encodes a graph in 𝒢_k. Further, for every k-vertex leafage chordal graph G and k > 1 in o(n^c), c > 0, we present a ((k-1)n log n + o(kn log n))-bit succinct data structure, constructed using the succinct data structure for path graphs with (k-1)n vertices. Our data structure supports adjacency query in O(k log n) time and using additional 2n log n bits, an O(k² d_v log n + log² n) time neighbourhood query where d_v is degree of v ∈ V.
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Girish Balakrishnan, Sankardeep Chakraborty, N. S. Narayanaswamy, and Kunihiko Sadakane. Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balakrishnan_et_al:LIPIcs.SWAT.2024.4,
  author =	{Balakrishnan, Girish and Chakraborty, Sankardeep and Narayanaswamy, N. S. and Sadakane, Kunihiko},
  title =	{{Succinct Data Structure for Chordal Graphs with Bounded Vertex Leafage}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.4},
  URN =		{urn:nbn:de:0030-drops-200446},
  doi =		{10.4230/LIPIcs.SWAT.2024.4},
  annote =	{Keywords: succinct data structure, chordal graphs, leafage, vertex leafage, path graphs}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.33
Space-Efficient Data Structure for Posets with Applications

Authors: Tatsuya Yanagita, Sankardeep Chakraborty, Kunihiko Sadakane, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Space efficient data structures for partial ordered sets or posets are well-researched field. It is known that a poset with n elements can be represented in n²/4 + o(n²) bits [Munro and Nicholson, 2016] and can also be represented in (1 + ε)n log n + 2nk + o(nk) bits [Farzan and Fischer, 2011] where k is width of the poset. In this paper, we make the latter data structure occupy 2n(k-1) + o(nk) bits by considering topological labeling on the elements of posets. Also considering the topological labeling, we propose a new data structure that calculates queries on transitive reduction graphs of posets faster though queries on transitive closure graphs are computed slower. Moreover, we propose an alternative data structure for topological labeled posets that calculates both of the queries faster though it uses 3nk - 2n + o(nk) bits of space. Additionally, we discuss the advantage of these data structures from the perspective of an application for BlockDAG, which is a more scalable version of Blockchain.
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Tatsuya Yanagita, Sankardeep Chakraborty, Kunihiko Sadakane, and Srinivasa Rao Satti. Space-Efficient Data Structure for Posets with Applications. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{yanagita_et_al:LIPIcs.SWAT.2022.33,
  author =	{Yanagita, Tatsuya and Chakraborty, Sankardeep and Sadakane, Kunihiko and Satti, Srinivasa Rao},
  title =	{{Space-Efficient Data Structure for Posets with Applications}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.33},
  URN =		{urn:nbn:de:0030-drops-161931},
  doi =		{10.4230/LIPIcs.SWAT.2022.33},
  annote =	{Keywords: Succinct Data Structures, Posets, Blockchain}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.29
Enumerating Range Modes

Authors: Kentaro Sumigawa, Sankardeep Chakraborty, Kunihiko Sadakane, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
Given a sequence of elements, we consider the problem of indexing the sequence to support range mode queries - given a query range, find the element with maximum frequency in the range. We give indexing data structures for this problem; given a sequence, we construct a data structure that can be used later to process arbitrary queries. Our algorithms are efficient for small maximum frequency cases. We also consider a natural generalization of the problem: the range mode enumeration problem, for which there has been no known efficient algorithms. Our algorithms have query time complexities which are linear in the output size plus small terms.
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Kentaro Sumigawa, Sankardeep Chakraborty, Kunihiko Sadakane, and Srinivasa Rao Satti. Enumerating Range Modes. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sumigawa_et_al:LIPIcs.ISAAC.2020.29,
  author =	{Sumigawa, Kentaro and Chakraborty, Sankardeep and Sadakane, Kunihiko and Satti, Srinivasa Rao},
  title =	{{Enumerating Range Modes}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.29},
  URN =		{urn:nbn:de:0030-drops-133732},
  doi =		{10.4230/LIPIcs.ISAAC.2020.29},
  annote =	{Keywords: range mode, space-efficient data structure, enumeration algorithm}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.67
Indexing Graph Search Trees and Applications

Authors: Sankardeep Chakraborty and Kunihiko Sadakane

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having n vertices and m edges while supporting various DFS related queries efficiently in the RAM with logarithmic word size. We study this problem in two well-known models: indexing and encoding models. While most of these queries can be supported easily in constant time using O(n lg n) bits of extra space, our goal here is, more specifically, to beat this trivial O(n lg n) bit space bound, yet not compromise too much on the running time of these queries. In the indexing model, the space bound of our solution involves the quantity m, hence, we obtain different bounds for sparse and dense graphs respectively. In the encoding model, we first give a space lower bound, followed by an almost optimal data structure with extremely fast query time. Central to our algorithm is a partitioning of the DFS tree into connected subtrees, and a compact way to store these connections. Finally, we also apply these techniques to compactly index the shortest path structure, biconnectivity structures among others.
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Sankardeep Chakraborty and Kunihiko Sadakane. Indexing Graph Search Trees and Applications. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2019.67,
  author =	{Chakraborty, Sankardeep and Sadakane, Kunihiko},
  title =	{{Indexing Graph Search Trees and Applications}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.67},
  URN =		{urn:nbn:de:0030-drops-110112},
  doi =		{10.4230/LIPIcs.MFCS.2019.67},
  annote =	{Keywords: Depth First Search Tree, Compact Data Structures, Encoding Schemes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.13
A Framework for In-place Graph Algorithms

Authors: Sankardeep Chakraborty, Anish Mukherjee, Venkatesh Raman, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Read-only memory (ROM) model is a classical model of computation to study time-space tradeoffs of algorithms. A classical result on the ROM model is that any algorithm to sort n numbers using O(s) words of extra space requires Omega (n^2/s) comparisons for lg n <= s <= n/lg n and the bound has also been recently matched by an algorithm. However, if we relax the model, we do have sorting algorithms (say Heapsort) that can sort using O(n lg n) comparisons using O(lg n) bits of extra space, even keeping a permutation of the given input sequence at anytime during the algorithm. We address similar relaxations for graph algorithms. We show that a simple natural relaxation of ROM model allows us to implement fundamental graph search methods like BFS and DFS more space efficiently than in ROM. By simply allowing elements in the adjacency list of a vertex to be permuted, we show that, on an undirected or directed connected graph G having n vertices and m edges, the vertices of G can be output in a DFS or BFS order using O(lg n) bits of extra space and O(n^3 lg n) time. Thus we obtain similar bounds for reachability and shortest path distance (both for undirected and directed graphs). With a little more (but still polynomial) time, we can also output vertices in the lex-DFS order. As reachability in directed graphs (even in DAGs) and shortest path distance (even in undirected graphs) are NL-complete, and lex-DFS is P-complete, our results show that our model is more powerful than ROM if L != P. En route, we also introduce and develop algorithms for another relaxation of ROM where the adjacency lists of the vertices are circular lists and we can modify only the heads of the lists. Here we first show a linear time DFS implementation using n + O(lg n) bits of extra space. Improving the extra space exponentially to only O(lg n) bits, we also obtain BFS and DFS albeit with a slightly slower running time. Both the models we propose maintain the graph structure throughout the algorithm, only the order of vertices in the adjacency list changes. In sharp contrast, for BFS and DFS, to the best of our knowledge, there are no algorithms in ROM that use even O(n^{1-epsilon}) bits of extra space; in fact, implementing DFS using cn bits for c<1 has been mentioned as an open problem. Furthermore, DFS (BFS, respectively) algorithms using n+o(n) (o(n), respectively) bits of extra use Reingold's [JACM, 2008] or Barnes et al's reachability algorithm [SICOMP, 1998] and hence have high runtime. Our results can be contrasted with the recent result of Buhrman et al. [STOC, 2014] which gives an algorithm for directed st-reachability on catalytic Turing machines using O(lg n) bits with catalytic space O(n^2 lg n) and time O(n^9).
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Sankardeep Chakraborty, Anish Mukherjee, Venkatesh Raman, and Srinivasa Rao Satti. A Framework for In-place Graph Algorithms. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chakraborty_et_al:LIPIcs.ESA.2018.13,
  author =	{Chakraborty, Sankardeep and Mukherjee, Anish and Raman, Venkatesh and Satti, Srinivasa Rao},
  title =	{{A Framework for In-place Graph Algorithms}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.13},
  URN =		{urn:nbn:de:0030-drops-94760},
  doi =		{10.4230/LIPIcs.ESA.2018.13},
  annote =	{Keywords: DFS, BFS, in-place algorithm, space-efficient graph algorithms, logspace}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.22
Biconnectivity, Chain Decomposition and st-Numbering Using O(n) Bits

Authors: Sankardeep Chakraborty, Venkatesh Raman, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014) reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of depth first search (DFS) of a graph on n vertices and m edges, taking O(m lg lg n) time using O(n) bits of space improving on the time bound of O(m lg n) due to Asano et al. Subsequently Banerjee et al. (COCOON 2016) gave an O(m + n) time implementation using O(m+n) bits, for DFS and its classical applications (including testing for biconnectivity, and finding cut vertices and cut edges). Recently, Kammer et al. (MFCS 2016) gave an algorithm for testing biconnectivity using O(n + min{m, n lg lg n}) bits in linear time. In this paper, we consider O(n) bits implementations of the classical applications of DFS. These include the problem of finding cut vertices, and biconnected components, chain decomposition and st-numbering. Classical algorithms for them typically use DFS and some Omega(lg n) bits of information at each node. Our O(n)-bit implementations for these problems take O(m lg^c n lg lg n) time for some small constant c (c leq 3). Central to our implementation is a succinct representation of the DFS tree and a space efficient partitioning of the DFS tree into connected subtrees, which maybe of independent interest for space efficient graph algorithms.
Cite as

Sankardeep Chakraborty, Venkatesh Raman, and Srinivasa Rao Satti. Biconnectivity, Chain Decomposition and st-Numbering Using O(n) Bits. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2016.22,
  author =	{Chakraborty, Sankardeep and Raman, Venkatesh and Satti, Srinivasa Rao},
  title =	{{Biconnectivity, Chain Decomposition and st-Numbering Using O(n) Bits}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.22},
  URN =		{urn:nbn:de:0030-drops-67927},
  doi =		{10.4230/LIPIcs.ISAAC.2016.22},
  annote =	{Keywords: biconnectivity, st-number, chain decomposition, tree cover, space efficient algorithms, read-only memory}
}
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