Streaming approximation resistance of every ordering CSP
Streaming approximation resistance of every ordering CSP
复制标题
每个排序CSP的流近似电阻
DOI：
10.4230/lipics.approx/random.2021.17
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Santhoshini Velusamy
中科院分区：
文献类型：
--
作者：
Noah G. Singer;M. Sudan;Santhoshini Velusamy
订购约束满意度问题（OCSP）由家庭$$ \ MATHCAL F $$定义
f
$$ \ {1，\ ldots，k \} $$上的谓词映射排列
{
1
，，，，
...
，，，，
k
}
to $$ \ {0,1 \} $$
{
0
，，，，
1
}
。
f
）在n个变量上，由约束列表组成，每个列表由$$ \ MATHCAL F $$的谓词组成
f
应用于k的不同变量。和“之间的最大”。
在这项工作中，我们考虑（单频）流设置中最大数量满足约束的任务，当实例作为约束流时。
f
，（$$ \ MATHCAL F $$
f
）与O（n）空间流算法相比，即使用O（n）空间的算法无法区分流的流，其中几乎每个约束都可以从no订购中可以按照明显的空间绑定在我们的结果中，要牢记在于各种因素。
ϵ
>
0
，不是$$（1/2+\ epsilon）$$
（（
1
/
2
+
ϵ
）
- 由于Guruswami＆Tao（2019），在O（n）空间中具有最佳最佳不Xibibibibity结果
o
（（
n
）
空间。
我们的结果基于Chou等人的最新作品（2022b，2024），他为广泛的“标准”（即非订购）约束满意度（CSP）提供了紧密的线性空间无Ximibibibibility定理（CSPS）有限）字母。
我们的结果是通过从任何给定的OCSP中建立适当的标准CSP家族（每个字母尺寸Q），并将自己的家庭应用于这个CSP家族，以将标准CSP的结果转换为OCSP，我们证明此较早定理的硬实例具有以下概率的“分区扩展”属性：对于n个变量的每个分区中，对于大多数约束，都变量在不同的块中。
An ordering constraint satisfaction problem (OCSP) is defined by a family $$\mathcal F$$
F
of predicates mapping permutations on $$\{1,\ldots,k\}$$
{
1
,
…
,
k
}
to $$\{0,1\}$$
{
0
,
1
}
. An instance of ($$\mathcal F$$
F
) on n variables consists of a list of constraints, each consisting of a predicate from $$\mathcal F$$
F
applied on k distinct variables. The goal is to find an ordering of the n variables that maximizes the number of constraints for which the induced ordering on the k variables satisfies the predicate. OCSPs capture well-studied problems including ‘maximum acyclic subgraph’ () and “maximum betweenness”.
In this work, we consider the task of approximating the maximum number of satisfiable constraints in the (single-pass) streaming setting, when an instance is presented as a stream of constraints. We show that for every $$\mathcal F$$
F
, ($$\mathcal F$$
F
) is approximation-resistant to o(n)-space streaming algorithms, i.e., algorithms using o(n) space cannot distinguish streams where almost every constraint is satisfiable from streams where no ordering beats the random ordering by a noticeable amount. This space bound is tight up to polylogarithmic factors. In the case of , our result shows that for every $$\epsilon>0$$
ϵ
>
0
, is not $$(1/2+\epsilon)$$
(
1
/
2
+
ϵ
)
-approximable in o(n) space. The previous best inapproximability result, due to Guruswami & Tao (2019), only ruled out 3/4-approximations in $$o(\sqrt n)$$
o
(
n
)
space.
Our results build on recent works of Chou et al. (2022b, 2024) who provide a tight, linear-space inapproximability theorem for a broad class of “standard” (i.e., non-ordering) constraint satisfaction problems (CSPs) over arbitrary (finite) alphabets.
Our results are obtained by building a family of appropriate standard CSPs (one for every alphabet size q) from any given OCSP and applying their theorem to this family of CSPs. To convert the resulting hardness results for standard CSPs back to our OCSP, we show that the hard instances from this earlier theorem have the following “partition expansion” property with high probability: For every partition of the n variables into small blocks, for most of the constraints, all variables are in distinct blocks.
用于近似 CSP 的线性空间流下界
DOI：
10.1145/3519935.3519983
发表时间：
2022
期刊：
{STOC} '22: 54th Annual {ACM} {SIGACT} Symposium on Theory of Computing
影响因子：
--
作者：
Chou, Chi-Ning;Golovnev, Alexander;Sudan, Madhu;Velingker, Ameya;Velusamy, Santhoshini
通讯作者：
Velusamy, Santhoshini
有向图流中的顶点排序问题
DOI：
10.1137/1.9781611975994.109
发表时间：
2020
期刊：
SODA
影响因子：
--
作者：
Chakrabarti, Amit;Ghosh, Prantar;McGregor, Andrew;Vorotnikova, Sofya
通讯作者：
Vorotnikova, Sofya