Information Processing Letters最新文献

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Total variation distance for product distributions is #P-complete

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2025-01-21 DOI: 10.1016/j.ipl.2025.106560

Arnab Bhattacharyya , Sutanu Gayen , Kuldeep S. Meel , Dimitrios Myrisiotis , A. Pavan , N.V. Vinodchandran

We show that computing the total variation distance between two product distributions is

# P

-complete. This is in stark contrast with other distance measures such as Kullback–Leibler, Chi-square, and Hellinger, which tensorize over the marginals leading to efficient algorithms.

引用次数: 0

On the Tractability Landscape of the Conditional Minisum Approval Voting Rule

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2025-01-21 DOI: 10.1016/j.ipl.2025.106561

Georgios Amanatidis , Michael Lampis , Evangelos Markakis , Georgios Papasotiropoulos

This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational complexity of this rule, demonstrating that no approach can significantly outperform the brute-force algorithm under common computational complexity assumptions and various natural input restrictions. In response, we propose two practical restrictions (the first in the literature) that make the problem computationally tractable and show that these restrictions are essentially tight. Overall, this work provides a clear picture of the tractability landscape of the problem, contributing to a comprehensive understanding of the complications introduced by conditional ballots and indicating that conditional approval voting can be applied in practice, albeit under specific conditions.

引用次数: 0

A lower bound for the Quickhull convex hull algorithm that disproves the Quickhull precision conjecture

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2025-01-14 DOI: 10.1016/j.ipl.2025.106558

Michael T. Goodrich

The Quickhull algorithm is a simple algorithm for constructing the convex hull of a set of n points. Quickhull is usually described for points in the plane, in which case it is defined as a divide-and-conquer algorithm, where one has a pair of points

(p, r)

such that p and r are on the convex hull, and one then finds the point, q, farthest from the line

\overline{p r}

, which must also be on the convex hull, and then uses the triangle

(p, q, r)

to divide the remaining points and recursively solve the resulting subproblems. It is well-known that Quickhull has a worst-case running time of

Θ (n^{2})

, but it runs much faster than this for some input distributions. In a highly cited paper, Barber, Dobkin, and Huhdanpaa conjecture that the Quickhull algorithm runs in worst-case

O (n \log h)

time, where h is the size of the convex hull, when the input points have precision

O (\log n)

. In this paper, we give an explicit lower-bound construction that shows that, in general, the worst-case running time of the Quickhull algorithm is

Θ (n h)

. Our lower bound proof also provides a counter-example to the Quickhull precision conjecture of Barber et al., in that we give an explicit construction of a set, S, of n points with precision

O (\log n)

such that h is

O (\log n)

but the worst-case running time of Quickhull on S is

Θ (n h)

, not

O (n \log h)

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引用次数: 0

String searching with mismatches using AVX2 and AVX-512 instructions

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2025-01-13 DOI: 10.1016/j.ipl.2025.106557

Tamanna Chhabra , Sukhpal Singh Ghuman , Jorma Tarhio

We present new algorithms for the k mismatches version of approximate string matching. Our algorithms utilize the SIMD (Single Instruction Multiple Data) instruction set extensions, particularly AVX2 and AVX-512 instructions. Our approach is an extension of an earlier algorithm for exact string matching with SSE2 and AVX2. In addition, we modify this exact string matching algorithm to work with AVX-512. We demonstrate the competitiveness of our solutions by practical experiments. Our algorithms outperform earlier algorithms for both exact and approximate string matching on various benchmark data sets.

引用次数: 0

On approximate reconfigurability of label cover

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2025-01-03 DOI: 10.1016/j.ipl.2024.106556

Naoto Ohsaka

Given a two-prover game G and its two satisfying labelings

ψ_{ini}

and

ψ_{tar}

, the Label Cover Reconfiguration problem asks whether

ψ_{ini}

can be transformed into

ψ_{tar}

by repeatedly changing the label of a single vertex while preserving any intermediate labeling satisfying G. We consider its optimization version by relaxing the feasibility of labelings, referred to as Maxmin Label Cover Reconfiguration: We are allowed to pass through any non-satisfying labelings, but required to maximize the “soundness error,” which is defined as the minimum fraction of satisfied edges during transformation from

ψ_{ini}

ψ_{tar}

. Since the parallel repetition theorem of Raz (1998) [32], which implies

-hardness of approximating Label Cover within any constant factor, gives strong inapproximability results for many

-hard problems, one may think of using Maxmin Label Cover Reconfiguration to derive inapproximability results for reconfiguration problems. We prove the following results on Maxmin Label Cover Reconfiguration, which display different trends from those of Label Cover and the parallel repetition theorem:

•
Maxmin Label Cover Reconfiguration can be approximated within a factor of $\frac{1}{4} - o (1)$ for some restricted graph classes, including biregular graphs, balanced bipartite graphs with no isolated vertices, and superconstant average degree graphs.
•
A “naive” parallel repetition of Maxmin Label Cover Reconfiguration does not decrease the soundness error for every two-prover game.
•
Label Cover Reconfiguration on projection games can be decided in polynomial time.

Our results suggest that a reconfiguration analogue of the parallel repetition theorem is unlikely.

{"title":"On approximate reconfigurability of label cover","authors":"Naoto Ohsaka","doi":"10.1016/j.ipl.2024.106556","DOIUrl":"10.1016/j.ipl.2024.106556","url":null,"abstract":"<div><div>Given a two-prover game G and its two satisfying labelings <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>ini</mi></mrow></msub></math> and <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>tar</mi></mrow></msub></math>, the Label Cover Reconfiguration problem asks whether <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>ini</mi></mrow></msub></math> can be transformed into <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>tar</mi></mrow></msub></math> by repeatedly changing the label of a single vertex while preserving any intermediate labeling satisfying G. We consider its optimization version by relaxing the feasibility of labelings, referred to as Maxmin Label Cover Reconfiguration: We are allowed to pass through any non-satisfying labelings, but required to maximize the “soundness error,” which is defined as the minimum fraction of satisfied edges during transformation from <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>ini</mi></mrow></msub></math> to <math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>tar</mi></mrow></msub></math>. Since the parallel repetition theorem of Raz (1998) [32], which implies <figure><img></figure>-hardness of approximating Label Cover within any constant factor, gives strong inapproximability results for many <figure><img></figure>-hard problems, one may think of using Maxmin Label Cover Reconfiguration to derive inapproximability results for reconfiguration problems. We prove the following results on Maxmin Label Cover Reconfiguration, which display different trends from those of Label Cover and the parallel repetition theorem:<ul><li>•<div>Maxmin Label Cover Reconfiguration can be approximated within a factor of <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> for some restricted graph classes, including biregular graphs, balanced bipartite graphs with no isolated vertices, and superconstant average degree graphs.</div></li><li>•<div>A “naive” parallel repetition of Maxmin Label Cover Reconfiguration does not decrease the soundness error for every two-prover game.</div></li><li>•<div>Label Cover Reconfiguration on projection games can be decided in polynomial time.</div></li></ul> Our results suggest that a reconfiguration analogue of the parallel repetition theorem is unlikely.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"189 ","pages":"Article 106556"},"PeriodicalIF":0.7,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Connected equitable cake division via Sperner's lemma

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-12-27 DOI: 10.1016/j.ipl.2024.106554

Umang Bhaskar , A.R. Sricharan , Rohit Vaish

We study the problem of fair cake-cutting where each agent receives a connected piece of the cake. A division of the cake is deemed fair if it is equitable, which means that all agents derive the same value from their assigned piece. Prior work has established the existence of a connected equitable division for agents with nonnegative valuations using various techniques. We provide a simple proof of this result using Sperner's lemma. Our proof extends known existence results for connected equitable divisions to significantly more general classes of valuations, including nonnegative valuations with externalities, as well as several interesting subclasses of general (possibly negative) valuations.

引用次数: 0

New bounds for the number of lightest cycles in undirected graphs

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-12-20 DOI: 10.1016/j.ipl.2024.106555

Hassene Aissi , Mourad Baiou , Francisco Barahona

Consider an undirected graph

G = (V, E)

with positive integer edge weights. Subramanian [11] established an upper bound of

| V |^{4} / 6

on the number of minimum weight cycles. We present a new algorithm to enumerate all minimum weight cycles with a complexity of

O (| V |^{3} (| E | + | V | \log | V |))

. Using this algorithm, we derive the following upper bounds for the number of minimum weight cycles: if the minimum weight is even, the bound is

| V |^{4} / 4

, and if it is odd, the bound is

| V |^{3} / 2

. Notably, we improve Subramanian's bound by an order of magnitude when the minimum weight of a cycle is odd. Additionally, we demonstrate that these bounds are asymptotically tight.

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引用次数: 0

Satisfying the restricted isometry property with the optimal number of rows and slightly less randomness

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-12-18 DOI: 10.1016/j.ipl.2024.106553

Shravas Rao

A matrix

Φ \in R^{Q \times N}

satisfies the restricted isometry property if

{‖ Φ x ‖}_{2}^{2}

is approximately equal to

{‖ x ‖}_{2}^{2}

for all k-sparse vectors x. We give a construction of RIP matrices with the optimal

Q = O (k \log (N / k))

rows using

O (k \log (N / k) \log (k))

bits of randomness. The main technical ingredient is an extension of the Hanson-Wright inequality to ε-biased distributions.

引用次数: 0

Improved hardness of approximation for Geometric Bin Packing

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-12-17 DOI: 10.1016/j.ipl.2024.106552

Arka Ray , Sai Sandeep

The Geometric Bin Packing (GBP) problem is a generalization of Bin Packing where the input is a set of d-dimensional rectangles, and the goal is to pack them into d-dimensional unit cubes efficiently. It is NP-hard to obtain a PTAS for the problem, even when

d = 2

. For general d, the best-known approximation algorithm has an approximation guarantee that is exponential in d. In contrast, the best hardness of approximation is still a small constant inapproximability from the case when

d = 2

. In this paper, we show that the problem cannot be approximated within a

d^{1 - ϵ}

factor unless

NP = P

Recently, d-dimensional Vector Bin Packing, a problem closely related to the GBP, was shown to be hard to approximate within a

Ω (\log d)

factor when d is a fixed constant, using a notion of Packing Dimension of set families. In this paper, we introduce a geometric analog of it, the Geometric Packing Dimension of set families. While we fall short of obtaining similar inapproximability results for the Geometric Bin Packing problem when d is fixed, we prove a couple of key properties of the Geometric Packing Dimension which highlight fundamental differences between Geometric Bin Packing and Vector Bin Packing.

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引用次数: 0

An efficient algorithm for identifying rainbow ortho-convex 4-sets in k-colored point sets

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters

Pub Date : 2024-12-10 DOI: 10.1016/j.ipl.2024.106551

David Flores-Peñaloza , Mario A. Lopez , Nestaly Marín , David Orden

Let P be a k-colored set of n points in the plane,

4 \leq k \leq n

. We study the problem of deciding if P contains a subset of four points of different colors such that its Rectilinear Convex Hull has positive area. We show this problem to be equivalent to deciding if there exists a point c in the plane such that each of the open quadrants defined by c contains a point of P, each of them having a different color. We provide an

O (n \log n)

-time algorithm for this problem, where the hidden constant does not depend on k; then, we prove that this problem has time complexity

Ω (n \log n)

in the algebraic computation tree model. No general position assumptions for P are required.

引用次数: 0

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