scholarly journals Incremental Symmetry Breaking Constraints for Graph Search Problems

2020 ◽  
Vol 34 (02) ◽  
pp. 1536-1543
Author(s):  
Avraham Itzhakov ◽  
Michael Codish
Keyword(s):  
Problem Solving ◽  
Symmetry Breaking ◽  
Special Property ◽  
Graph Search ◽  
Search Problem ◽  
Search Problems ◽  
Canonical Order ◽  
Parallel Graph ◽  
Canonical Graph

This paper introduces incremental symmetry breaking constraints for graph search problems which are complete and compact. We show that these constraints can be computed incrementally: A symmetry breaking constraint for order n graphs can be extended to one for order n + 1 graphs. Moreover, these constraints induce a special property on their canonical solutions: An order n canonical graph contains a canonical subgraph on the first k vertices for every 1 ≤ k ≤ n. This facilitates a “generate and extend” paradigm for parallel graph search problem solving: To solve a graph search problem φ on order n graphs, first generate the canonical graphs of some order k < n. Then, compute canonical solutions for φ by extending, in parallel, each canonical order k graph together with suitable symmetry breaking constraints. The contribution is that the proposed symmetry breaking constraints enable us to extend the order k canonical graphs to order n canonical solutions. We demonstrate our approach through its application on two hard graph search problems.

scholarly journals Combinatorial Nullstellensatz Modulo Prime Powers and the Parity Argument

10.37236/4124 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
László Varga
Keyword(s):  
Complexity Class ◽  
Combinatorial Nullstellensatz ◽  
Search Problem ◽  
Search Problems ◽  
Computational Search

We present new generalizations of Olson's theorem and of a consequence of Alon's Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove that the problem of finding degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and the search problem corresponding to the Combinatorial Nullstellensatz over $\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).

scholarly journals Learning Descriptors Invariance through Equivalence Relations within Manifold: A New Approach to Expression Invariant 3D Face Recognition

2020 ◽  
Vol 6 (11) ◽  
pp. 112
Author(s):  
Faisal R. Al-Osaimi
Keyword(s):  
Search Algorithm ◽  
Recognition Performance ◽  
Feature Space ◽  
Training Data ◽  
Equivalence Relations ◽  
Graph Search ◽  
Search Problem ◽  
New Approach ◽  
Unique Approach ◽  
Training Examples

This paper presents a unique approach for the dichotomy between useful and adverse variations of key-point descriptors, namely the identity and the expression variations in the descriptor (feature) space. The descriptors variations are learned from training examples. Based on labels of the training data, the equivalence relations among the descriptors are established. Both types of descriptor variations are represented by a graph embedded in the descriptor manifold. Invariant recognition is then conducted as a graph search problem. A heuristic graph search algorithm suitable for the recognition under this setup was devised. The proposed approach was tested on the FRGC v2.0, the Bosphorus and the 3D TEC datasets. It has shown to enhance the recognition performance, under expression variations, by considerable margins.

scholarly journals Human Search in a Fitness Landscape: How to Assess the Difficulty of a Search Problem

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Oana Vuculescu ◽  
Mads Kock Pedersen ◽  
Jacob F. Sherson ◽  
Carsten Bergenholtz
Keyword(s):  
Problem Solving ◽  
Computational Modeling ◽  
Cultural Evolution ◽  
Fitness Landscape ◽  
Search Behavior ◽  
Search Problem ◽  
Distinct Component ◽  
New Type ◽  
Human Problem ◽  
The Continuum

Computational modeling is widely used to study how humans and organizations search and solve problems in fields such as economics, management, cultural evolution, and computer science. We argue that current computational modeling research on human problem-solving needs to address several fundamental issues in order to generate more meaningful and falsifiable contributions. Based on comparative simulations and a new type of visualization of how to assess the nature of the fitness landscape, we address two key assumptions that approaches such as the NK framework rely on: that the NK captures the continuum of the complexity of empirical fitness landscapes and that search behavior is a distinct component, independent from the topology of the fitness landscape. We show the limitations of the most common approach to conceptualize how complex, or rugged, a landscape is, as well as how the nature of the fitness landscape is fundamentally intertwined with search behavior. Finally, we outline broader implications for how to simulate problem-solving.

An improved version of the AAG cryptographic protocol

2019 ◽  
Vol 11 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Vitaliĭ Roman’kov
Keyword(s):  
Linear Span ◽  
Original Version ◽  
Search Problem ◽  
Cryptographic Protocol ◽  
Membership Problem ◽  
Search Problems ◽  
Hard Problems ◽  
Cryptographic Key ◽  
Conjugacy Search Problem ◽  
Conjugacy Search

AbstractAn improved version of the Anshel–Anshel–Goldfeld (AAG) algebraic cryptographic key-exchange scheme, that is in particular resistant against the Tsaban linear span cryptanalysis, is established. Unlike the original version, that is based on the intractability of the simultaneous conjugacy search problem for the platform group, the proposed version is based on harder simultaneous membership-conjugacy search problems, and the membership problem needs to be solved for a subset of the platform group that can be easily and efficiently built to be very complicated and without any good structure. A number of other hard problems need to be solved first before start solving the simultaneous membership-conjugacy search problem to obtain the exchanged key.

Parallel graph search: application to intraretinal layer segmentation of 3-D macular OCT scans

2012 ◽  
Author(s):  
Kyungmoo Lee ◽  
Michael D. Abràmoff ◽  
Mona K. Garvin ◽  
Milan Sonka
Keyword(s):  
Graph Search ◽  
Layer Segmentation ◽  
Parallel Graph

scholarly journals Gastroscopic Image Graph: Application to Noninvasive Multitarget Tracking under Gastroscopy

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Wang ◽  
Weiling Hu ◽  
Jiquan Liu ◽  
Jianmin Si ◽  
Huilong Duan
Keyword(s):  
Disease Diagnosis ◽  
Optical Biopsy ◽  
Graph Search ◽  
Gastric Disease ◽  
Multitarget Tracking ◽  
Search Problem ◽  
Stomach Body ◽  
Attractive Candidate ◽  
The Mean

Gastroscopic examination is one of the most common methods for gastric disease diagnosis. In this paper, a multitarget tracking approach is proposed to assist endoscopists in identifying lesions under gastroscopy. This approach analyzes numerous preobserved gastroscopic images and constructs a gastroscopic image graph. In this way, the deformation registration between gastroscopic images is regarded as a graph search problem. During the procedure, the endoscopist marks suspicious lesions on the screen and the graph is utilized to locate and display the lesions in the appropriate frames based on the calculated registration model. Compared to traditional gastroscopic lesion surveillance methods (e.g., tattooing or probe-based optical biopsy), this approach is noninvasive and does not require additional instruments. In order to assess and quantify the performance, this approach was applied to stomach phantom data andin vivodata. The clinical experimental results demonstrated that the accuracy at angularis, antral, and stomach body was 6.3 ± 2.4 mm, 7.6 ± 3.1 mm, and 7.9 ± 1.6 mm, respectively. The mean accuracy was 7.31 mm, average targeting time was 56 ms, and thePvalue was 0.032, which makes it an attractive candidate for clinical practice. Furthermore, this approach provides a significant reference for endoscopic target tracking of other soft tissue organs.

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