7 Search Results for "Uchizawa, Kei"

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.33
Coloring Reconfiguration Under Color Swapping

Authors: Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the Coloring Reconfiguration problem, we are given two proper k-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: single-vertex recoloring and Kempe chain recoloring. In this paper, we introduce a new rule, called color swapping, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to k: the problem is solvable in polynomial time for k ≤ 2, and is PSPACE-complete for k ≥ 3. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when k = 3, for split graphs when k is fixed, and for cographs when k is arbitrary.
Cite as

Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura. Coloring Reconfiguration Under Color Swapping. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fuchs_et_al:LIPIcs.ISAAC.2025.33,
  author =	{Fuchs, Janosch and Saito, Rin and Suga, Tatsuhiro and Suzuki, Takahiro and Tamura, Yuma},
  title =	{{Coloring Reconfiguration Under Color Swapping}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.33},
  URN =		{urn:nbn:de:0030-drops-249411},
  doi =		{10.4230/LIPIcs.ISAAC.2025.33},
  annote =	{Keywords: Combinatorial reconfiguration, graph coloring, PSPACE-complete, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.57
Improved Hardness-Of-Approximation for Token-Swapping

Authors: Sam Hiken and Nicole Wein

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study the token swapping problem, in which we are given a graph with an initial assignment of one distinct token to each vertex, and a final desired assignment (again with one token per vertex). The goal is to find the minimum length sequence of swaps of adjacent tokens required to get from the initial to the final assignment. The token swapping problem is known to be NP-complete. It is also known to have a polynomial-time 4-approximation algorithm. From the hardness-of-approximation side, it is known to be NP-hard to approximate with a ratio better than 1001/1000. Our main result is an improvement of the approximation ratio of the lower bound: We show that it is NP-hard to approximate with ratio better than 14/13. We then turn our attention to the 0/1-weighted version, in which every token has a weight of either 0 or 1, and the cost of a swap is the sum of the weights of the two participating tokens. Unlike standard token swapping, no constant-factor approximation is known for this version, and we provide an explanation. We prove that 0/1-weighted token swapping is NP-hard to approximate with ratio better than (1-ε) ln(n) for any constant ε > 0. Lastly, we prove two barrier results for the standard (unweighted) token swapping problem. We show that one cannot beat the current best known approximation ratio of 4 using a large class of algorithms which includes all known algorithms, nor can one beat it using a common analysis framework.
Cite as

Sam Hiken and Nicole Wein. Improved Hardness-Of-Approximation for Token-Swapping. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hiken_et_al:LIPIcs.ESA.2025.57,
  author =	{Hiken, Sam and Wein, Nicole},
  title =	{{Improved Hardness-Of-Approximation for Token-Swapping}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.57},
  URN =		{urn:nbn:de:0030-drops-245251},
  doi =		{10.4230/LIPIcs.ESA.2025.57},
  annote =	{Keywords: algorithms, token-swapping, hardness-of-approximation, lower-bounds}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.73
Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position

Authors: Anastasiia Tkachenko and Haitao Wang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Given a set P of n points in the plane, its unit-disk graph G(P) is a graph with P as its vertex set such that two points of P are connected by an edge if their (Euclidean) distance is at most 1. We consider several classical problems on G(P) in a special setting when points of P are in convex position. These problems are all NP-hard in the general case. We present efficient algorithms for these problems under the convex position assumption. ● For the problem of finding the smallest dominating set of G(P), we present an O(knlog n) time algorithm, where k is the smallest dominating set size. We also consider the weighted case in which each point of P has a weight and the goal is to find a dominating set in G(P) with minimum total weight; our algorithm runs in O(n³log² n) time. In particular, for a given k, our algorithm can compute in O(kn²log² n) time a minimum weight dominating set of size at most k (if it exists). ● For the discrete k-center problem, which is to find a subset of k points in P (called centers) for a given k, such that the maximum distance between any point in P and its nearest center is minimized. We present an algorithm that solves the problem in O(min{n^{4/3}log n+knlog² n,k² nlog²n}) time, which is O(n²log² n) in the worst case when k = Θ(n). For comparison, the runtime of the current best algorithm for the continuous version of the problem where centers can be anywhere in the plane is O(n³ log n). ● For the problem of finding a maximum independent set in G(P), we give an algorithm of O(n^{7/2}) time and another randomized algorithm of O(n^{37/11}) expected time, which improve the previous best result of O(n⁶log n) time. Our algorithms can be extended to compute a maximum-weight independent set in G(P) with the same time complexities when points of P have weights. - If we are looking for an (unweighted) independent set of size 3, we derive an algorithm of O(nlog n) time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position). - If points of P have weights and are not necessarily in convex position, we present an algorithm that can find a maximum-weight independent set of size 3 in O(n^{5/3+δ}) time for an arbitrarily small constant δ > 0. By slightly modifying the algorithm, a maximum-weight clique of size 3 can also be found within the same time complexity. ● For the dispersion problem, which is to find a subset of k points from P for a given k, such that the minimum pairwise distance of the points in the subset is maximized. We present an algorithm of O(n^{7/2}log n) time and another randomized algorithm of O(n^{37/11}log n) expected time, which improve the previous best result of O(n⁶) time. - If k = 3, we present an algorithm of O(nlog² n) time and another randomized algorithm of O(nlog n) expected time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position).
Cite as

Anastasiia Tkachenko and Haitao Wang. Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tkachenko_et_al:LIPIcs.STACS.2025.73,
  author =	{Tkachenko, Anastasiia and Wang, Haitao},
  title =	{{Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.73},
  URN =		{urn:nbn:de:0030-drops-228982},
  doi =		{10.4230/LIPIcs.STACS.2025.73},
  annote =	{Keywords: Dominating set, k-center, geometric set cover, independent set, clique, vertex cover, unit-disk graphs, convex position, dispersion, maximally separated sets}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.85
Exponential Lower Bounds for Threshold Circuits of Sub-Linear Depth and Energy

Authors: Kei Uchizawa and Haruki Abe

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here, the energy of a circuit measures sparsity of their computation, and is defined as the maximum number of gates outputting non-zero values taken over all the input assignments. As our main result, we prove that any threshold circuit C of size s, depth d, energy e and weight w satisfies log(rk(M_C)) ≤ ed (log s + log w + log n), where rk(M_C) is the rank of the communication matrix M_C of a 2n-variable Boolean function that C computes. Thus, such a threshold circuit C is able to compute only a Boolean function of which communication matrix has rank bounded by a product of logarithmic factors of s, w and linear factors of d, e. This implies an exponential lower bound on the size of even sublinear-depth and sublinear-energy threshold circuit. For example, we can obtain an exponential lower bound s = 2^Ω(n^{1/3}) for threshold circuits of depth n^{1/3}, energy n^{1/3} and weight 2^o(n^{1/3}). We also show that the inequality is tight up to a constant factor when the depth d and energy e satisfies ed = o(n/log n). For other models of neural networks such as a discretized ReLU circuits and descretized sigmoid circuits, we define energy as the maximum number of gates outputting non-zero values. We then prove that a similar inequality also holds for a discretized circuit C: rk(M_C) = O(ed(log s + log w + log n)³). Thus, if we consider the number gates outputting non-zero values as a measure for sparse activity of a neural network, our results suggest that larger depth linearly helps neural networks to acquire sparse activity.
Cite as

Kei Uchizawa and Haruki Abe. Exponential Lower Bounds for Threshold Circuits of Sub-Linear Depth and Energy. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 85:1-85:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{uchizawa_et_al:LIPIcs.MFCS.2023.85,
  author =	{Uchizawa, Kei and Abe, Haruki},
  title =	{{Exponential Lower Bounds for Threshold Circuits of Sub-Linear Depth and Energy}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{85:1--85:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.85},
  URN =		{urn:nbn:de:0030-drops-186192},
  doi =		{10.4230/LIPIcs.MFCS.2023.85},
  annote =	{Keywords: Circuit complexity, disjointness function, equality function, neural networks, threshold circuits, ReLU cicuits, sigmoid circuits, sparse activity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.54
Size, Depth and Energy of Threshold Circuits Computing Parity Function

Authors: Kei Uchizawa

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

Abstract
We investigate relations among the size, depth and energy of threshold circuits computing the n-variable parity function PAR_n, where the energy is a complexity measure for sparsity on computation of threshold circuits, and is defined to be the maximum number of gates outputting "1" over all the input assignments. We show that PAR_n is hard for threshold circuits of small size, depth and energy: - If a depth-2 threshold circuit C of size s and energy e computes PAR_n, it holds that 2^{n/(elog ^e n)} ≤ s; and - if a threshold circuit C of size s, depth d and energy e computes PAR_n, it holds that 2^{n/(e2^{e+d}log ^e n)} ≤ s. We then provide several upper bounds: - PAR_n is computable by a depth-2 threshold circuit of size O(2^{n-2e}) and energy e; - PAR_n is computable by a depth-3 threshold circuit of size O(2^{n/(e-1)} + 2^{e-2}) and energy e; and - PAR_n is computable by a threshold circuit of size O((e+d)2^{n-m}), depth d + O(1) and energy e + O(1), where m = max (((e-1)/(d-1))^{d-1}, ((d-1)/(e-1))^{e-1}). Our lower and upper bounds imply that threshold circuits need exponential size if both depth and energy are constant, which contrasts with the fact that PAR_n is computable by a threshold circuit of size O(n) and depth 2 if there is no restriction on the energy. Our results also suggest that any threshold circuit computing the parity function needs depth to be sparse if its size is bounded.
Cite as

Kei Uchizawa. Size, Depth and Energy of Threshold Circuits Computing Parity Function. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{uchizawa:LIPIcs.ISAAC.2020.54,
  author =	{Uchizawa, Kei},
  title =	{{Size, Depth and Energy of Threshold Circuits Computing Parity Function}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{54:1--54:13},
  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.2020.54},
  URN =		{urn:nbn:de:0030-drops-133988},
  doi =		{10.4230/LIPIcs.ISAAC.2020.54},
  annote =	{Keywords: Circuit complexity, neural networks, threshold circuits, sprase activity, tradeoffs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.76
Synchronous Boolean Finite Dynamical Systems on Directed Graphs over XOR Functions

Authors: Mitsunori Ogihara and Kei Uchizawa

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
In this paper, we investigate the complexity of a number of computational problems defined on a synchronous boolean finite dynamical system, where update functions are chosen from a template set of exclusive-or and its negation. We first show that the reachability and path-intersection problems are solvable in logarithmic space-uniform AC¹ if the objects execute permutations, while the reachability problem is known to be in P and the path-intersection problem to be in UP in general. We also explore the case where the reachability or intersection are tested on a subset of objects, and show that this hardens complexity of the problems: both problems become NP-complete, and even Π^p₂-complete if we further require universality of the intersection. We next consider the exact cycle length problem, that is, determining whether there exists an initial configuration that yields a cycle in the configuration space having exactly a given length, and show that this problem is NP-complete. Lastly, we consider the t-predecessor and t-Garden of Eden problem, and prove that these are solvable in polynomial time even if the value of t is also given in binary as part of instance, and the two problems are in logarithmic space-uniform NC² if the value of t is given in unary as part of instance.
Cite as

Mitsunori Ogihara and Kei Uchizawa. Synchronous Boolean Finite Dynamical Systems on Directed Graphs over XOR Functions. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 76:1-76:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ogihara_et_al:LIPIcs.MFCS.2020.76,
  author =	{Ogihara, Mitsunori and Uchizawa, Kei},
  title =	{{Synchronous Boolean Finite Dynamical Systems on Directed Graphs over XOR Functions}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{76:1--76:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.76},
  URN =		{urn:nbn:de:0030-drops-127543},
  doi =		{10.4230/LIPIcs.MFCS.2020.76},
  annote =	{Keywords: Computational complexity, dynamical systems, Garden of Eden, predecessor, reachability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.8
Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems

Authors: Akinori Kawachi, Mitsunori Ogihara, and Kei Uchizawa

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
A Boolean Finite Synchronous Dynamical System (BFDS, for short) consists of a finite number of objects that each maintains a boolean state, where after individually receiving state assignments, the objects update their state with respect to object-specific time-independent boolean functions synchronously in discrete time steps. The present paper studies the computational complexity of determining, given a boolean finite synchronous dynamical system, a configuration, which is a boolean vector representing the states of the objects, and a positive integer t, whether there exists another configuration from which the given configuration can be reached in t steps. It was previously shown that this problem, which we call the t-Predecessor Problem, is NP-complete even for t = 1 if the update function of an object is either the conjunction of arbitrary fan-in or the disjunction of arbitrary fan-in. This paper studies the computational complexity of the t-Predecessor Problem for a variety of sets of permissible update functions as well as for polynomially bounded t. It also studies the t-Garden-Of-Eden Problem, a variant of the t-Predecessor Problem that asks whether a configuration has a t-predecessor, which itself has no predecessor. The paper obtains complexity theoretical characterizations of all but one of these problems.
Cite as

Akinori Kawachi, Mitsunori Ogihara, and Kei Uchizawa. Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kawachi_et_al:LIPIcs.MFCS.2017.8,
  author =	{Kawachi, Akinori and Ogihara, Mitsunori and Uchizawa, Kei},
  title =	{{Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.8},
  URN =		{urn:nbn:de:0030-drops-81078},
  doi =		{10.4230/LIPIcs.MFCS.2017.8},
  annote =	{Keywords: Computational complexity, dynamical systems, Garden of Eden, predecessor}
}
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