岩間研究室 発表論文
2010年度
[ 論文誌 ]
- id=2010-06
- K. Iwama, K. Seto, and S. Tamaki,
- ``The Planar Hajos Calculus for Bounded Degree Graphs'',
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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.E93-A, no.6, pp.1000--1007, Jun. 2010.
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>> Abstract
- id=2010-14
- David Manlove, Robert W. Irving, and Kazuo Iwama,
- ``Guest Editorial: Special Issue on Matching Under Preferences.'',
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Algorithmica, vol.58, no.1, pp.1--4, Sep. 2010.
- id=2010-15
- Kazuo Iwama, and Guochuan Zhang,
- ``Online knapsack with resource augmentation.'',
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Inf. Process. Lett., vol.110, no.22, pp.1016--1020, Oct. 2010.
- id=2010-16
- K. Makino, S. Tamaki, and M. Yamamoto,
- ``On the Boolean Connectivity Problem for Horn Relations'',
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Discrete Applied Mathematics, vol.158, no.18, pp.2024--2030, Nov. 2010.
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>> Abstract
- id=2010-17
- K. Iwama, S. Miyazaki, and H. Yanagisawa,
- ``Approximation Algorithms for the Sex-Equal Stable Marriage Problem'',
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ACM Transactions on Algorithms, vol.7, 1/2, Nov. 2010.
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>> Abstract
- id=2010-22
- Hiroshi Fujiwara, Kazuo Iwama, and Yoshiyuki Sekiguchi,
- ``Average-case competitive analyses for one-way trading.'',
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Journal of Combinatorial Optimization, vol.21, no.1, pp.83--107, Jan. 2011.
- id=2010-20
- Wolfgang W. Bein, Kazuo Iwama, Jun Kawahara, Lawrence L. Larmore, and James A. Oravec,
- ``A randomized algorithm for two servers in cross polytope spaces.'',
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Theoretical Computer Science, vol.412, no.7, pp.563-572, Feb. 2011.
- id=2010-28
- Y. Yoshida, and H. Ito,
- ``Property testing on k-vertex connectivity of graphs'',
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Algorithmica, vol.to appear., , (発表月不明) .
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>> Abstract
[ 国際会議 ]
- id=2010-01
- H. Ito, J. Teruyama, and Y. Yoshida,
- ``An Almost Optimal Algorithm for Winkler's Sorting Pairs in Bins'',
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Proc. of the 3rd Asian Association for Algorithms and Computation (AAAC 2010), pp., Apr. 2010.
- id=2010-02
- K. Iwama, K. Seto, and S. Tamaki,
- ``Enumerating Non-3-colorable Planar Graphs by the Haj坦s Calculus'',
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Proc. of the 3rd Asian Association for Algorithms and Computation (AAAC 2010), pp.24, Apr. 2010.
- id=2010-03
- K. Iwama, T. Takai, and S. Tamaki,
- ``Improved Randomized Algorithms for 3-SAT'',
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Proc. of the 3rd Asian Association for Algorithms and Computation (AAAC 2010), pp.41, Apr. 2010.
- id=2010-04
- H. Morizumi,
- ``The Size and Width of Boolean Circuits'',
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Proc. of the 3rd Asian Association for Algorithms and Computation (AAAC 2010), pp.45, Apr. 2010.
- id=2010-05
- Kazuo Iwama, H. Nishimura, R. Raymond, and J. Teruyama,
- ``Quantum Counterfeit Coin Problems'',
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Proc. of the 3rd Asian Association for Algorithms and Computation (AAAC 2010), pp., Apr. 2010.
- id=2010-08
- K. Makino, S. Tamaki, and M. Yamamoto,
- ``An Exact Algorithm for the Boolean Connectivity Problem for k-CNF'',
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The 13th International Conference on Theory and Applications of Satisfiability Testing Proc. SAT 2010, LNCS 6175, pp.172--180, Jul. 2010.
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>> Abstract
- id=2010-10
- K. Ueno,
- ``Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds'',
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Proc. 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010), LNCS 6281, pp.665--676, Aug. 2010.
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>> Abstract
- id=2010-11
- S. Tamaki, and Y. Yoshida,
- ``A Query Efficient Non-Adaptive Long Code Test with Perfect Completeness'',
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Proc. 14th Intl. Workshop on Randomization and Computation (RANDOM 2010), pp.738--751, Sep. 2010.
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>> Abstract
- id=2010-12
- Y. Yoshida, and H. Ito,
- ``Testing Outerplanarity of Bounded Degree Graphs'',
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Proc. 14th Intl. Workshop on Randomization and Computation (RANDOM 2010), pp.642--655, Sep. 2010.
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>> Abstract
- id=2010-13
- K. Iwama, S. Miyazaki, and H. Yanagisawa,
- ``A 25/17-Approximation Algorithm for the Stable Marriage Problem with One-Sided Ties'',
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Proc. 18th Annual European Symposium on Algorithms (ESA 2010), LNCS 6347, pp.135--146, Sep. 2010.
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>> Abstract
- id=2010-18
- K. Iwama, K. Seto, T. Takai, and S. Tamaki,
- ``Improved Randomized Algorithms for 3-SAT'',
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The 21st International Symposium on Algorithms and Computation (ISAAC 2010), LNCS 6506, pp.73--84, Dec. 2010.
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>> Abstract
- id=2010-19
- K. Iwama, H. Nishimura, R. Raymond, and J. Teruyama,
- ``Quantum Counterfeit Coin Problems'',
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The 21st International Symposium on Algorithms and Computation (ISAAC 2010), LNCS 6506, pp.85--96, Dec. 2010.
- id=2010-20
- Y. Yoshida,
- ``Optimal Constant-Time Approximation Algorithms and (Unconditional)
Inapproximability Results for Every Bounded-Degree CSP'',
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Proc. 43rd ACM Symposium on Theory of Computing (STOC 2011), pp.665--674, Jan. 2011.
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>> Abstract
- id=2010-21
- Y. Yoshida,
- ``Lower Bounds on Query Complexity for Testing Bounded-Degree CSPs'',
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Proc. 26th IEEE Conference on Computational Complexity (CCC 2011), pp.34--44, Jan. 2011.
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>> Abstract
[ 国内発表 ]
- id=2010-09
- 玉置卓,
- ``3SATに対する乱択アルゴリズムの改良'',
- ERATO湊離散構造処理系+NEO 合同研究会, 2010年 7月.
- id=2010-23
- H. Ito, J. Teruyama, Y. Yoshida,
- ``Bubble Sort with Infinitely Large Bins'',
- 冬のLAシンポジウム, pp.25.1--25.7, 2011年 2月.
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>> Abstract
- id=2010-25
- 伊藤大雄, 清島奨, 吉田悠一,
- ``ナップサック問題に対する定数時間近似アルゴリズム'',
- 電子情報通信学会 コンピューテーション研究会, 信学技報, vol.110, no.464, COMP2010-51, pp.29--36, 2011年 3月.
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>> Abstract
- id=2010-26
- 吉田悠一,
- ``次数制限モデルにおける全てのCSPに対する最適な定数時間近似アルゴリズムと近似困難性'',
- 電子情報通信学会 総合大会, vol., pp.(to appear), 2011年 3月.
- id=2010-27
- R. Cleve, K. Iwama, F. Le Gall, H. Nishimura, S. Tani, J. Teruyama, S. Yamashita,
- ``Reconstructing Strings from Substrings with Quantum Query'',
- 電子情報通信学会 総合大会, vol., pp.S-21--S-22, 2011年 3月.
[ その他 ]
- id=2010-07
- K. Iwama, S. Miyazaki, and H. Yanagisawa,
- ``A 25/17-Approximation Algorithm for the Stable Marriage Problem with One-Sided Ties'',
- IBM Research Report RT0913, Jun. 2010.
- id=2010-24
- K. Makino, S. Tamaki, and M. Yamamoto,
- ``Derandomizing HSSW algorithm for 3-SAT'',
- arXiv:1102.3766v1 [cs.CC], Feb. 2011.
- id=2010-29
- H. Ito, S. Tanigawa, and Y. Yoshida,
- ``Constant-Time Algorithms for Sparsity Matroids'',
- arXiv:1103.2581v1 [cs.CC], Mar. 2011.
Abstract
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id=2010-06
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The planar Haj\'os calculus (\phc) is the Haj\'os calculus with the
restriction that all the graphs that appear in the construction
(including a final graph) must be planar.
The degree-$d$ planar Haj\'os calculus (\phcd{d}) is \phc \ with the
restriction that all the graphs that appear in the construction
(including a final graph) must have maximum degree at most $d$.
We prove the followings:
(1) If \phc \ is polynomially bounded, then for any $d \geq 4$,
\phcd{d+2} \ can generate any non-3-colorable planar graphs of maximum
degree at most $d$ in polynomial steps.
(2) If \phc \ can generate any non-3-colorable planar graphs of maximum
degree 4 in polynomial steps, then \phc \ is polynomially bounded.
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id=2010-08
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We present an exact algorithm for a PSPACE-complete problem,
denoted by $\CONN k\SAT$,
which asks if the solution space for a given $k$-CNF formula
is connected on the $n$-dimensional hypercube.
The problem is known to be PSPACE-complete for $k\geq 3$,
and polynomial solvable for $k\leq 2$ \cite{GKMP06}.
We show that
$\CONN k\SAT$ for $k\geq 3$ is solvable
in time $O((2-\epsilon_k)^n)$ for some constant $\epsilon_k>0$,
where $\epsilon_k$ depends only on $k$, but not on $n$.
This result is considered to be interesting due to the following fact
shown by \cite{Cal09}:
QBF-3-SAT,
which is a typical PSPACE-complete problem,
is not solvable in time $O((2-\epsilon)^n)$ for any constant $\epsilon>0$,
provided that the SAT problem (with no restriction to the clause length)
is not solvable in time $O((2-\epsilon)^n)$ for any constant $\epsilon>0$.
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id=2010-10
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Karchmer, Kushilevitz and Nisan formulated the formula size problem as
an integer programming problem called the rectangle bound and
introduced a technique called the LP bound, which gives a formula size
lower bound by showing a feasible solution of the dual problem of its
LP-relaxation. As extensions of the LP bound, we introduce novel
general techniques proving formula size lower bounds, named a
quasi-additive bound and the Sherali-Adams bound. While the
Sherali-Adams bound is potentially strong enough to give a lower bound
matching to the rectangle bound, we prove that the quasi-additive
bound can surpass the rectangle bound.
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id=2010-11
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Long Code testing is a fundamental problem in the area of property testing and hardness of approximation.
Long Code is a function of the form $f(x)=x_i$ for some index $i$.
In the Long Code testing, the problem is, given oracle access to a collection of Boolean functions,
to decide whether all the functions are the same Long Code, or cross-influences of any two functions are small.
In this paper, we study the following problem:
How small the soundness $s$ of the Long Code test with perfect completeness can be by using non-adaptive $q$ queries?
We give a Long Code test with $s=(2q+3)/2^q$, where $q$ is of the form $2^k-1$ for any integer $k>2$.
Our test is a ``noisy'' version of Samorodnitsky-Trevisan's Hyper Graph linearity test with suitably chosen noise distribution.
To bound the soundness, we use Invariance-Principle style analysis in the spirit of O'Donnell and Wu (STOC 2009).
Previously, H\r{a}stad and Khot (Theory of Computing, 2005) have shown $s=2^{4\sqrt{q}}/2^q$ for infinitely many $q$.
Chen (RANDOM 2009) has improved this to $s=q^3/2^q$ for infinitely many $q$ with ``adaptive'' queries.
As for the Long Code test with ``almost'' perfect completeness,
Samorodnitsky and Trevisan (SICOMP, 2009) have shown $s=2q/2^q$ (or even $(q+1)/2^q$ for infinitely many $q$).
Austrin and Mossel (Computational Complexity, 2009) have improved this to $s=(q+o(q))/2^q$ (or even $(q+4)/2^q$
assuming the famous Hadamard Conjecture) for any $q$.
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id=2010-12
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We present an efficient algorithm for testing outerplanarity of graphs in the bounded degree model.
In this model, given a graph $G$ with $n$ vertices and degree bound $d$,
we should distinguish with high probability the case that $G$ is outerplanar from the case
that modifying at least an $\epsilon$-fraction of the edge set of $G$ is necessary to make $G$ outerplanar.
Our algorithm runs in $\tilde{O}\left(\frac{1}{\epsilon^{13}d^6}+\frac{d}{\epsilon^2}\right)$ time, which is independent of the size of graphs.
This is the first algorithm for a non-trivial minor-closed property whose time complexity is polynomial in $\frac{1}{\epsilon}$ and $d$.
To achieve the time complexity,
we exploit the tree-like structure inherent to an outerplanar graph using the microtree/macrotree decomposition of a tree.
As a corollary, we also show an algorithm that tests whether a given graph is
a cactus with time complexity $\tilde{O}\left(\frac{1}{\epsilon^{13}d^6}+\frac{d}{\epsilon^2}\right)$.
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id=2010-13
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The problem of finding a largest stable matching where preference lists
may include ties and unacceptable partners (MAX SMTI) is known to be
NP-hard. It cannot be approximated within $33/29 \ (> 1.1379)$ unless
P=NP, and the current best approximation algorithm achieves the ratio
of $1.5$. MAX SMTI remains NP-hard even when preference lists of one side
do not contain ties, and it cannot be approximated within $21/19 \ (> 1.1052)$ unless P=NP.
However, even under this restriction, the best known approximation ratio is still $1.5$.
In this paper, we improve it to $25/17 \ (< 1.4706)$.
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id=2010-16
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Gopalan {\em et~al.} studied in [Proceedings of the 33rd International Colloquium on Automata,
Languages and Programming (ICALP 2006), pp. 346--357, 2006] and
[SIAM J. Comput., 38(6):2330--2355, 2009]
connectivity properties of the solution-space of
Boolean formulas, and investigated complexity issues on the
connectivity problems in Schaefer's framework.
A set $S$ of logical relations is $\schaefer$
if all relations in $S$
are either bijunctive, Horn, dual Horn, or affine.
They first conjectured that
the connectivity problem for $\schaefer$ is in $\P$.
We disprove their conjecture by showing that
there exists a set $S$ of Horn relations
such that the connectivity problem for $S$ is $\coNP$-complete.
We also investigate a tractable aspect of Horn and dual Horn relations
with respect to characteristic sets.
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id=2010-17
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The stable marriage problem is a classical matching problem introduced
by Gale and Shapley. It is known that for any instance, there exists
a solution, and there is a polynomial time algorithm to find one.
However, the matching obtained by this algorithm is man-optimal, that
is, the matching is favorable for men but unfavorable for women,
(or, if we exchange the roles of men and women, the resulting matching
is woman-optimal). The sex-equal stable marriage problem, posed by
Gusfield and Irving, seeks a stable matching ``fair'' for both
genders. Specifically it seeks a stable matching with the property
that the sum of the men's scores is as close as possible to that of the
women's. This problem is known to be strongly NP-hard.
In this paper, we give a polynomial time algorithm for finding {\em a
near optimal} solution for the sex-equal stable marriage problem.
Furthermore, we consider the problem of optimizing an additional
criterion: among stable matchings that are near optimal in terms of
the sex-equality, find a minimum egalitarian stable matching. We show
that this problem is strongly NP-hard, and give a polynomial time
algorithm whose approximation ratio is less than two.
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id=2010-18
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This pager gives a new randomized algorithm which solves 3-SAT in time
$O(1.32113^n)$.
The previous best bound is $O(1.32216^n)$ due to Rolf (J.~SAT,~2006).
The new algorithm uses the same approach as Iwama and Tamaki
(SODA~2004), but exploits the non-uniform initial assignment due to
Hofmeister et al. (STACS 2002) against the Sch\"oning's local search
(FOCS~1999).
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id=2010-20
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Raghavendra (STOC 2008) gave an elegant and surprising result: if
Khot's Unique Games Conjecture (STOC 2002) is true, then for every
constraint satisfaction problem (CSP), the best approximation ratio is
attained by a certain simple semidefinite programming and a rounding
scheme for it.
In this paper, we show that similar results hold for constant-time
approximation algorithms in the bounded-degree model. Specifically, we
present the followings: (i) For every CSP, we construct an oracle that
serves an access, in constant time, to a nearly optimal solution to a
basic LP relaxation of the CSP. (ii) Using the oracle, we give a
constant-time rounding scheme that achieves an approximation ratio
coincident with the integrality gap of the basic LP. (iii) Finally, we
give a generic conversion from integrality gaps of basic LPs to
hardness results. All of those results are \textit{unconditional}.
Therefore, for every bounded-degree CSP, we give the best
constant-time approximation algorithm among all.
A CSP instance is called $\epsilon$-far from satisfiability if we must
remove at least an $\epsilon$-fraction of constraints to make it
satisfiable. A CSP is called testable if there is a constant-time
algorithm that distinguishes satisfiable instances from $\epsilon$-far
instances with probability at least $2/3$. Using the results above,
we also derive, under a technical assumption, an equivalent condition
under which a CSP is testable in the bounded-degree model.
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id=2010-21
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In this paper, we consider lower bounds on the query complexity for
testing CSPs in the bounded-degree model. We mainly consider Boolean
CSPs allowing literals.
First, for any ``symmetric'' predicate $P:\{0,1\}^{k}\to \{0,1\}$
except \textsf{EQU} where $k\geq 3$, we show that every (randomized)
algorithm that distinguishes satisfiable instances of
\textsf{CSP}($P$) from instances $(|P^{-1}(0)|/2^k-\epsilon)$-far from
satisfiability requires $\Omega(n^{1/2+\delta})$ queries where $n$ is
the number of variables and $\delta>0$ is a constant that depends on
$P$ and $\epsilon$. This breaks a natural lower bound
$\Omega(n^{1/2})$, which is obtained by the birthday paradox. We also
show that every one-sided error tester requires $\Omega(n)$ queries
for such $P$. These results are hereditary in the sense that the same
results hold for any predicate $Q$ such that $P^{-1}(1)\subseteq
Q^{-1}(1)$. For \textsf{EQU}, we give a one-sided error tester whose
query complexity is $\tilde{O}(n^{1/2})$. Also, for \textsf{$2$-XOR}
(or, equivalently \textsf{E2LIN2}), we show an
$\Omega(n^{1/2+\delta})$ lower bound for distinguishing instances
between $\epsilon$-close to and $(1/2-\epsilon)$-far from
satisfiability.
Next, for the general \textsf{$k$-CSP} over the binary domain, we show
that every algorithm that distinguishes satisfiable instances from
instances $(1-2k/2^k-\epsilon)$-far from satisfiability requires
$\Omega(n)$ queries. The matching NP-hardness is not known, even
assuming the Unique Games Conjecture or the $d$-to-$1$ Conjecture. As
a corollary, for \mislong on graphs with $n$ vertices and a degree
bound $d$, we show that every approximation algorithm within a factor
$d/\poly\log d$ and an additive error of $\epsilon n$ requires
$\Omega(n)$ queries. Previously, only super-constant lower bounds were
known.
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id=2010-23
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id=2010-25
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id=2010-28
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We present an algorithm for testing the $k$-vertex-connectivity of
graphs with the given maximum degree. The time complexity of the
algorithm is independent of the number of vertices and edges of
graphs. Fixed degree bound $d$, a graph $G$ with $n$ vertices and a
maximum degree at most $d$ is called $\epsilon$-far from
$k$-vertex-connectivity when at least $\frac{\epsilon dn}{2}$ edges
must be added to or removed from $G$ to obtain a $k$-vertex-connected
graph with a maximum degree at most $d$. The algorithm always accepts
every graph that is $k$-vertex-connected and rejects every graph that
is $\epsilon$-far from $k$-vertex-connectivity with a probability of
at least $2/3$. The algorithm runs in $O\left(d\left(\frac{c}{\epsilon
d}\right)^{k}\log\frac{1}{\epsilon d}\right)$ time $(c>1 \mbox{ is a
constant})$ for $(k-1)$-vertex-connected graphs, and in
$O\left(d\left(\frac{ck}{\epsilon d}\right)^{k}\log\frac{k}{\epsilon
d}\right)$ time $(c>1 \mbox{ is a constant})$ for general graphs. It
is the first constant-time $k$-vertex-connectivity testing algorithm
for general $k\geq 4$.