49 Search Results for "Weimann, Oren"

Volume

LIPIcs, Volume 161

31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

CPM 2020, June 17-19, 2020, Copenhagen, Denmark

Editors: Inge Li Gørtz and Oren Weimann

Document
DOI: 10.4230/LIPIcs.ESA.2023.4
What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?

Authors: Amir Abboud, Shay Mozes, and Oren Weimann

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The Voronoi diagrams technique, introduced by Cabello [SODA'17] to compute the diameter of planar graphs in subquadratic time, has revolutionized the field of distance computations in planar graphs. We present novel applications of this technique in static, fault-tolerant, and partially-dynamic undirected unweighted planar graphs, as well as some new limitations. - In the static case, we give n^{3+o(1)}/D² and Õ(n⋅D²) time algorithms for computing the diameter of a planar graph G with diameter D. These are faster than the state of the art Õ(n^{5/3}) [SODA'18] when D < n^{1/3} or D > n^{2/3}. - In the fault-tolerant setting, we give an n^{7/3+o(1)} time algorithm for computing the diameter of G⧵ {e} for every edge e in G (the replacement diameter problem). This should be compared with the naive Õ(n^{8/3}) time algorithm that runs the static algorithm for every edge. - In the incremental setting, where we wish to maintain the diameter while adding edges, we present an algorithm with total running time n^{7/3+o(1)}. This should be compared with the naive Õ(n^{8/3}) time algorithm that runs the static algorithm after every update. - We give a lower bound (conditioned on the SETH) ruling out an amortized O(n^{1-ε}) update time for maintaining the diameter in weighted planar graph. The lower bound holds even for incremental or decremental updates. Our upper bounds are obtained by novel uses and manipulations of Voronoi diagrams. These include maintaining the Voronoi diagram when edges of the graph are deleted, allowing the sites of the Voronoi diagram to lie on a BFS tree level (rather than on boundaries of r-division), and a new reduction from incremental diameter to incremental distance oracles that could be of interest beyond planar graphs. Our lower bound is the first lower bound for a dynamic planar graph problem that is conditioned on the SETH.
Cite as

Amir Abboud, Shay Mozes, and Oren Weimann. What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 4:1-4:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{abboud_et_al:LIPIcs.ESA.2023.4,
  author =	{Abboud, Amir and Mozes, Shay and Weimann, Oren},
  title =	{{What Else Can Voronoi Diagrams Do for Diameter in Planar Graphs?}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.4},
  URN =		{urn:nbn:de:0030-drops-186575},
  doi =		{10.4230/LIPIcs.ESA.2023.4},
  annote =	{Keywords: Planar graphs, diameter, dynamic graphs, fault tolerance}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.27
Improved Compression of the Okamura-Seymour Metric

Authors: Shay Mozes, Nathan Wallheimer, and Oren Weimann

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Let G = (V,E) be an undirected unweighted planar graph. Let S = {s_1,…,s_k} be the vertices of some face in G and let T ⊆ V be an arbitrary set of vertices. The Okamura-Seymour metric compression problem asks to compactly encode the S-to-T distances. Consider a vector storing the distances from an arbitrary vertex v to all vertices S = {s_1,…,s_k} in their cyclic order. The pattern of v is obtained by taking the difference between every pair of consecutive values of this vector. In STOC'19, Li and Parter used a VC-dimension argument to show that in planar graphs, the number of distinct patterns, denoted p_#, is only O(k³). This resulted in a simple Õ(min{k⁴+|T|, k⋅|T|}) space compression of the Okamura-Seymour metric. We give an alternative proof of the p_# = O(k³) bound that exploits planarity beyond the VC-dimension argument. Namely, our proof relies on cut-cycle duality, as well as on the fact that distances among vertices of S are bounded by k. Our method implies the following: (1) An Õ(p_#+k+|T|) space compression of the Okamura-Seymour metric, thus improving the compression of Li and Parter to Õ(min{k³+|T|, k⋅|T|}). (2) An optimal Õ(k+|T|) space compression of the Okamura-Seymour metric, in the case where the vertices of T induce a connected component in G. (3) A tight bound of p_# = Θ(k²) for the family of Halin graphs, whereas the VC-dimension argument is limited to showing p_# = O(k³).
Cite as

Shay Mozes, Nathan Wallheimer, and Oren Weimann. Improved Compression of the Okamura-Seymour Metric. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 27:1-27:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mozes_et_al:LIPIcs.ISAAC.2022.27,
  author =	{Mozes, Shay and Wallheimer, Nathan and Weimann, Oren},
  title =	{{Improved Compression of the Okamura-Seymour Metric}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.27},
  URN =		{urn:nbn:de:0030-drops-173123},
  doi =		{10.4230/LIPIcs.ISAAC.2022.27},
  annote =	{Keywords: Shortest paths, planar graphs, metric compression, distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.35
Approximate Circular Pattern Matching

Authors: Panagiotis Charalampopoulos, Tomasz Kociumaka, Jakub Radoszewski, Solon P. Pissis, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We investigate the complexity of approximate circular pattern matching (CPM, in short) under the Hamming and edit distance. Under each of these two basic metrics, we are given a length-n text T, a length-m pattern P, and a positive integer threshold k, and we are to report all starting positions (called occurrences) of fragments of T that are at distance at most k from some cyclic rotation of P. In the decision version of the problem, we are to check if there is any such occurrence. All previous results for approximate CPM were either average-case upper bounds or heuristics, with the exception of the work of Charalampopoulos et al. [CKP^+, JCSS'21], who considered only the Hamming distance. For the reporting version of the approximate CPM problem, under the Hamming distance we improve upon the main algorithm of [CKP^+, JCSS'21] from 𝒪(n+(n/m) ⋅ k⁴) to 𝒪(n+(n/m) ⋅ k³ log log k) time; for the edit distance, we give an 𝒪(nk²)-time algorithm. Notably, for the decision versions and wide parameter-ranges, we give algorithms whose complexities are almost identical to the state-of-the-art for standard (i.e., non-circular) approximate pattern matching: - For the decision version of the approximate CPM problem under the Hamming distance, we obtain an 𝒪(n+(n/m) ⋅ k² log k / log log k)-time algorithm, which works in 𝒪(n) time whenever k = 𝒪(√{m log log m / log m}). In comparison, the fastest algorithm for the standard counterpart of the problem, by Chan et al. [CGKKP, STOC’20], runs in 𝒪(n) time only for k = 𝒪(√m). We achieve this result via a reduction to a geometric problem by building on ideas from [CKP^+, JCSS'21] and Charalampopoulos et al. [CKW, FOCS'20]. - For the decision version of the approximate CPM problem under the edit distance, the 𝒪(nklog³ k) runtime of our algorithm near matches the 𝒪(nk) runtime of the Landau-Vishkin algorithm [LV, J. Algorithms'89] for approximate pattern matching under edit distance; the latter algorithm remains the fastest known for k = Ω(m^{2/5}). As a stepping stone, we propose an 𝒪(nklog³ k)-time algorithm for solving the Longest Prefix k'-Approximate Match problem, proposed by Landau et al. [LMS, SICOMP'98], for all k' ∈ {1,…,k}. Our algorithm is based on Tiskin’s theory of seaweeds [Tiskin, Math. Comput. Sci.'08], with recent advancements (see Charalampopoulos et al. [CKW, FOCS'22]), and on exploiting the seaweeds' relation to Monge matrices. In contrast, we obtain a conditional lower bound that suggests a polynomial separation between approximate CPM under the Hamming distance over the binary alphabet and its non-circular counterpart. We also show that a strongly subquadratic-time algorithm for the decision version of approximate CPM under edit distance would refute the Strong Exponential Time Hypothesis.
Cite as

Panagiotis Charalampopoulos, Tomasz Kociumaka, Jakub Radoszewski, Solon P. Pissis, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Approximate Circular Pattern Matching. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 35:1-35:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ESA.2022.35,
  author =	{Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Radoszewski, Jakub and Pissis, Solon P. and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Approximate Circular Pattern Matching}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.35},
  URN =		{urn:nbn:de:0030-drops-169738},
  doi =		{10.4230/LIPIcs.ESA.2022.35},
  annote =	{Keywords: approximate circular pattern matching, Hamming distance, edit distance}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.4
The Fine-Grained Complexity of Episode Matching

Authors: Philip Bille, Inge Li Gørtz, Shay Mozes, Teresa Anna Steiner, and Oren Weimann

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
Given two strings S and P, the Episode Matching problem is to find the shortest substring of S that contains P as a subsequence. The best known upper bound for this problem is Õ(nm) by Das et al. (1997), where n,m are the lengths of S and P, respectively. Although the problem is well studied and has many applications in data mining, this bound has never been improved. In this paper we show why this is the case by proving that no O((nm)^{1-ε}) algorithm (even for binary strings) exists, unless the Strong Exponential Time Hypothesis (SETH) is false. We then consider the indexing version of the problem, where S is preprocessed into a data structure for answering episode matching queries P. We show that for any τ, there is a data structure using O(n+(n/(τ)) ^k) space that answers episode matching queries for any P of length k in O(k⋅ τ ⋅ log log n) time. We complement this upper bound with an almost matching lower bound, showing that any data structure that answers episode matching queries for patterns of length k in time O(n^δ), must use Ω(n^{k-kδ-o(1)}) space, unless the Strong k-Set Disjointness Conjecture is false. Finally, for the special case of k = 2, we present a faster construction of the data structure using fast min-plus multiplication of bounded integer matrices.
Cite as

Philip Bille, Inge Li Gørtz, Shay Mozes, Teresa Anna Steiner, and Oren Weimann. The Fine-Grained Complexity of Episode Matching. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 4:1-4:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bille_et_al:LIPIcs.CPM.2022.4,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Mozes, Shay and Steiner, Teresa Anna and Weimann, Oren},
  title =	{{The Fine-Grained Complexity of Episode Matching}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.4},
  URN =		{urn:nbn:de:0030-drops-161312},
  doi =		{10.4230/LIPIcs.CPM.2022.4},
  annote =	{Keywords: Pattern matching, fine-grained complexity, longest common subsequence}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.48
An Almost Optimal Edit Distance Oracle

Authors: Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, and Oren Weimann

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

Abstract
We consider the problem of preprocessing two strings S and T, of lengths m and n, respectively, in order to be able to efficiently answer the following queries: Given positions i,j in S and positions a,b in T, return the optimal alignment score of S[i..j] and T[a..b]. Let N = mn. We present an oracle with preprocessing time N^{1+o(1)} and space N^{1+o(1)} that answers queries in log^{2+o(1)}N time. In other words, we show that we can efficiently query for the alignment score of every pair of substrings after preprocessing the input for almost the same time it takes to compute just the alignment of S and T. Our oracle uses ideas from our distance oracle for planar graphs [STOC 2019] and exploits the special structure of the alignment graph. Conditioned on popular hardness conjectures, this result is optimal up to subpolynomial factors. Our results apply to both edit distance and longest common subsequence (LCS). The best previously known oracle with construction time and size 𝒪(N) has slow Ω(√N) query time [Sakai, TCS 2019], and the one with size N^{1+o(1)} and query time log^{2+o(1)}N (using a planar graph distance oracle) has slow Ω(N^{3/2}) construction time [Long & Pettie, SODA 2021]. We improve both approaches by roughly a √ N factor.
Cite as

Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, and Oren Weimann. An Almost Optimal Edit Distance Oracle. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 48:1-48:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2021.48,
  author =	{Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren},
  title =	{{An Almost Optimal Edit Distance Oracle}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{48:1--48:20},
  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.2021.48},
  URN =		{urn:nbn:de:0030-drops-141175},
  doi =		{10.4230/LIPIcs.ICALP.2021.48},
  annote =	{Keywords: longest common subsequence, edit distance, planar graphs, Voronoi diagrams}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.7
1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete

Authors: Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, and Avi Zeff

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
Consider n²-1 unit-square blocks in an n × n square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable - a variation of Rush Hour with only 1 × 1 cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle. By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically. Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color Subway Shuffle.
Cite as

Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, and Avi Zeff. 1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 7:1-7:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brunner_et_al:LIPIcs.FUN.2021.7,
  author =	{Brunner, Josh and Chung, Lily and Demaine, Erik D. and Hendrickson, Dylan and Hesterberg, Adam and Suhl, Adam and Zeff, Avi},
  title =	{{1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.7},
  URN =		{urn:nbn:de:0030-drops-127681},
  doi =		{10.4230/LIPIcs.FUN.2021.7},
  annote =	{Keywords: puzzles, sliding blocks, PSPACE-hardness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.5
On the Fine-Grained Complexity of Parity Problems

Authors: Amir Abboud, Shon Feller, and Oren Weimann

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

Abstract
We consider the parity variants of basic problems studied in fine-grained complexity. We show that finding the exact solution is just as hard as finding its parity (i.e. if the solution is even or odd) for a large number of classical problems, including All-Pairs Shortest Paths (APSP), Diameter, Radius, Median, Second Shortest Path, Maximum Consecutive Subsums, Min-Plus Convolution, and 0/1-Knapsack. A direct reduction from a problem to its parity version is often difficult to design. Instead, we revisit the existing hardness reductions and tailor them in a problem-specific way to the parity version. Nearly all reductions from APSP in the literature proceed via the (subcubic-equivalent but simpler) Negative Weight Triangle (NWT) problem. Our new modified reductions also start from NWT or a non-standard parity variant of it. We are not able to establish a subcubic-equivalence with the more natural parity counting variant of NWT, where we ask if the number of negative triangles is even or odd. Perhaps surprisingly, we justify this by designing a reduction from the seemingly-harder Zero Weight Triangle problem, showing that parity is (conditionally) strictly harder than decision for NWT.
Cite as

Amir Abboud, Shon Feller, and Oren Weimann. On the Fine-Grained Complexity of Parity Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 5:1-5:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abboud_et_al:LIPIcs.ICALP.2020.5,
  author =	{Abboud, Amir and Feller, Shon and Weimann, Oren},
  title =	{{On the Fine-Grained Complexity of Parity Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{5:1--5:19},
  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.2020.5},
  URN =		{urn:nbn:de:0030-drops-124127},
  doi =		{10.4230/LIPIcs.ICALP.2020.5},
  annote =	{Keywords: All-pairs shortest paths, Fine-grained complexity, Diameter, Distance product, Min-plus convolution, Parity problems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.57
Minimum Cut in O(m log² n) Time

Authors: Paweł Gawrychowski, Shay Mozes, and Oren Weimann

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

Abstract
We give a randomized algorithm that finds a minimum cut in an undirected weighted m-edge n-vertex graph G with high probability in O(m log² n) time. This is the first improvement to Karger’s celebrated O(m log³ n) time algorithm from 1996. Our main technical contribution is a deterministic O(m log n) time algorithm that, given a spanning tree T of G, finds a minimum cut of G that 2-respects (cuts two edges of) T.
Cite as

Paweł Gawrychowski, Shay Mozes, and Oren Weimann. Minimum Cut in O(m log² n) Time. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 57:1-57:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gawrychowski_et_al:LIPIcs.ICALP.2020.57,
  author =	{Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren},
  title =	{{Minimum Cut in O(m log² n) Time}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{57:1--57:15},
  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.2020.57},
  URN =		{urn:nbn:de:0030-drops-124646},
  doi =		{10.4230/LIPIcs.ICALP.2020.57},
  annote =	{Keywords: Minimum cut, Minimum 2-respecting cut}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CPM.2020
LIPIcs, Volume 161, CPM 2020, Complete Volume

Authors: Inge Li Gørtz and Oren Weimann

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
LIPIcs, Volume 161, CPM 2020, Complete Volume
Cite as

Inge Li Gørtz and Oren Weimann. LIPIcs, Volume 161, CPM 2020, Complete Volume. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 1-418, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@Proceedings{gortz_et_al:LIPIcs.CPM.2020,
  title =	{{LIPIcs, Volume 161, CPM 2020, Complete Volume}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{1--418},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020},
  URN =		{urn:nbn:de:0030-drops-121245},
  doi =		{10.4230/LIPIcs.CPM.2020},
  annote =	{Keywords: LIPIcs, Volume 161, CPM 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.CPM.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Inge Li Gørtz and Oren Weimann

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

Inge Li Gørtz and Oren Weimann. Front Matter, Table of Contents, Preface, Conference Organization. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 0:i-0:xvi, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gortz_et_al:LIPIcs.CPM.2020.0,
  author =	{G{\o}rtz, Inge Li and Weimann, Oren},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.0},
  URN =		{urn:nbn:de:0030-drops-121252},
  doi =		{10.4230/LIPIcs.CPM.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CPM.2020.1
Algebraic Algorithms for Finding Patterns in Graphs (Invited Talk)

Authors: Thore Husfeldt

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
I will give a gentle introduction to algebraic graph algorithms by showing how to determine if a given graph contains a simple path of length k. This is a famous problem admitting a beautiful and widely-known algorithm, namely the colour-coding method of Alon, Yuster and Zwick (1995). Starting from this entirely combinatorial approach, I will carefully develop an algebraic perspective on the same problem. First, I will explain how the colour-coding algorithm can be understood as the evaluation of a well-known expression (sometimes called the "walk-sum" of the graph) in a commutative algebra called the zeon algebra. From there, I will introduce the exterior algebra and present the algebraic framework recently developed with Brand and Dell (2018). The presentation is aimed at a combinatorially-minded audience largely innocent of abstract algebra.
Cite as

Thore Husfeldt. Algebraic Algorithms for Finding Patterns in Graphs (Invited Talk). In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, p. 1:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{husfeldt:LIPIcs.CPM.2020.1,
  author =	{Husfeldt, Thore},
  title =	{{Algebraic Algorithms for Finding Patterns in Graphs}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.1},
  URN =		{urn:nbn:de:0030-drops-121261},
  doi =		{10.4230/LIPIcs.CPM.2020.1},
  annote =	{Keywords: paths, exterior algebra, wedge product, color-coding, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.2
Finding the Anticover of a String

Authors: Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, and Kunihiro Wasa

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ≥ 3. We also show that the problem admits a polynomial-time solution for k=2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time using polynomial space.
Cite as

Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, and Kunihiro Wasa. Finding the Anticover of a String. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 2:1-2:11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alzamel_et_al:LIPIcs.CPM.2020.2,
  author =	{Alzamel, Mai and Conte, Alessio and Denzumi, Shuhei and Grossi, Roberto and Iliopoulos, Costas S. and Kurita, Kazuhiro and Wasa, Kunihiro},
  title =	{{Finding the Anticover of a String}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{2:1--2:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.2},
  URN =		{urn:nbn:de:0030-drops-121270},
  doi =		{10.4230/LIPIcs.CPM.2020.2},
  annote =	{Keywords: Anticover, String algorithms, Stringology, NP-complete}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.3
Double String Tandem Repeats

Authors: Amihood Amir, Ayelet Butman, Gad M. Landau, Shoshana Marcus, and Dina Sokol

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
A tandem repeat is an occurrence of two adjacent identical substrings. In this paper, we introduce the notion of a double string, which consists of two parallel strings, and we study the problem of locating all tandem repeats in a double string. The problem introduced here has applications beyond actual double strings, as we illustrate by solving two different problems with the algorithm of the double string tandem repeats problem. The first problem is that of finding all corner-sharing tandems in a 2-dimensional text, defined by Apostolico and Brimkov. The second problem is that of finding all scaled tandem repeats in a 1d text, where a scaled tandem repeat is defined as a string UU' such that U' is discrete scale of U. In addition to the algorithms for exact tandem repeats, we also present algorithms that solve the problem in the inexact sense, allowing up to k mismatches. We believe that this framework will open a new perspective for other problems in the future.
Cite as

Amihood Amir, Ayelet Butman, Gad M. Landau, Shoshana Marcus, and Dina Sokol. Double String Tandem Repeats. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 3:1-3:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{amir_et_al:LIPIcs.CPM.2020.3,
  author =	{Amir, Amihood and Butman, Ayelet and Landau, Gad M. and Marcus, Shoshana and Sokol, Dina},
  title =	{{Double String Tandem Repeats}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{3:1--3:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.3},
  URN =		{urn:nbn:de:0030-drops-121283},
  doi =		{10.4230/LIPIcs.CPM.2020.3},
  annote =	{Keywords: double string, tandem repeat, 2-dimensional, scale}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.4
Efficient Tree-Structured Categorical Retrieval

Authors: Djamal Belazzougui and Gregory Kucherov

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
We study a document retrieval problem in the new framework where D text documents are organized in a category tree with a pre-defined number h of categories. This situation occurs e.g. with taxomonic trees in biology or subject classification systems for scientific literature. Given a string pattern p and a category (level in the category tree), we wish to efficiently retrieve the t categorical units containing this pattern and belonging to the category. We propose several efficient solutions for this problem. One of them uses n(logσ(1+o(1))+log D+O(h)) + O(Δ) bits of space and O(|p|+t) query time, where n is the total length of the documents, σ the size of the alphabet used in the documents and Δ is the total number of nodes in the category tree. Another solution uses n(logσ(1+o(1))+O(log D))+O(Δ)+O(Dlog n) bits of space and O(|p|+tlog D) query time. We finally propose other solutions which are more space-efficient at the expense of a slight increase in query time.
Cite as

Djamal Belazzougui and Gregory Kucherov. Efficient Tree-Structured Categorical Retrieval. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 4:1-4:11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{belazzougui_et_al:LIPIcs.CPM.2020.4,
  author =	{Belazzougui, Djamal and Kucherov, Gregory},
  title =	{{Efficient Tree-Structured Categorical Retrieval}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{4:1--4:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.4},
  URN =		{urn:nbn:de:0030-drops-121299},
  doi =		{10.4230/LIPIcs.CPM.2020.4},
  annote =	{Keywords: pattern matching, document retrieval, category tree, space-efficient data structures}
}
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