528 research outputs found
Recognizing When Heuristics Can Approximate Minimum Vertex Covers Is Complete for Parallel Access to NP
For both the edge deletion heuristic and the maximum-degree greedy heuristic,
we study the problem of recognizing those graphs for which that heuristic can
approximate the size of a minimum vertex cover within a constant factor of r,
where r is a fixed rational number. Our main results are that these problems
are complete for the class of problems solvable via parallel access to NP. To
achieve these main results, we also show that the restriction of the vertex
cover problem to those graphs for which either of these heuristics can find an
optimal solution remains NP-hard.Comment: 16 pages, 2 figure
The Complexity of Computing Minimal Unidirectional Covering Sets
Given a binary dominance relation on a set of alternatives, a common thread
in the social sciences is to identify subsets of alternatives that satisfy
certain notions of stability. Examples can be found in areas as diverse as
voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08]
proved that it is NP-hard to decide whether an alternative is contained in some
inclusion-minimal upward or downward covering set. For both problems, we raise
this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and
provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other
natural problems regarding minimal or minimum-size covering sets are hard or
complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of
our results is that neither minimal upward nor minimal downward covering sets
(even when guaranteed to exist) can be computed in polynomial time unless P=NP.
This sharply contrasts with Brandt and Fischer's result that minimal
bidirectional covering sets (i.e., sets that are both minimal upward and
minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure
Complexity of certificates, heuristics, and counting types , with applications to cryptography and circuit theory
In dieser Habilitationsschrift werden Struktur und Eigenschaften von Komplexitätsklassen wie P und NP untersucht, vor allem im Hinblick auf: Zertifikatkomplexität, Einwegfunktionen, Heuristiken gegen NP-Vollständigkeit und Zählkomplexität. Zum letzten Punkt werden speziell untersucht: (a) die Komplexität von Zähleigenschaften von Schaltkreisen, (b) Separationen von Zählklassen mit Immunität und (c) die Komplexität des Zählens der Lösungen von ,,tally`` NP-Problemen
Discrete Algorithms for Analysis of Genotype Data
Accessibility of high-throughput genotyping technology makes possible genome-wide association studies for common complex diseases. When dealing with common diseases, it is necessary to search and analyze multiple independent causes resulted from interactions of multiple genes scattered over the entire genome. The optimization formulations for searching disease-associated risk/resistant factors and predicting disease susceptibility for given case-control study have been introduced. Several discrete methods for disease association search exploiting greedy strategy and topological properties of case-control studies have been developed. New disease susceptibility prediction methods based on the developed search methods have been validated on datasets from case-control studies for several common diseases. Our experiments compare favorably the proposed algorithms with the existing association search and susceptibility prediction methods
Broadcasting Protocol for Effective Data Dissemination in Vehicular Ad Hoc Networks
VANET topology is very dynamic due to frequent movements of the nodes. Using beacon information connected dominated set are formed and nodes further enhanced with neighbor elimination scheme. With acknowledgement the inter section issues are solve. A modified Broadcast Conquest and Delay De-synchronization mechanism address the broadcasting storm issues. Although data dissemination is possible in all direction, the performance of data dissemination in the opposite direction is investigated and compared against the existing protocols
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Traveling Salesman Problem
This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering
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