130 research outputs found
A comparative analysis between two heuristic algorithms for the graph vertex coloring problem
This study focuses on two heuristic algorithms for the graph vertex coloring problem: the sequential (greedy) coloring algorithm (SCA) and the Welsh–Powell algorithm (WPA). The code of the algorithms is presented and discussed. The methodology and conditions of the experiments are presented. The execution time of the algorithms was calculated as the average of four different starts of the algorithms for all analyzed graphs, taking into consideration the multitasking mode of the operating system. In the graphs with less than 600 vertices, in 90% of cases, both algorithms generated the same solutions. In only 10% of cases, the WPA algorithm generates better solutions. However, in the graphs with more than 1,000 vertices, in 35% of cases, the WPA algorithm generates better solutions. The results show that the difference in the execution time of the algorithms for all graphs is acceptable, but the quality of the solutions generated by the WPA algorithm in more than 20% of cases is better compared to the SC algorithm. The results also show that the quality of the solutions is not related to the number of iterations performed by the algorithms
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Approximation Algorithms for NP-Hard Problems
The workshop was concerned with the most important recent developments in the area of efficient approximation algorithms for NP-hard optimization problems as well as with new techniques for proving intrinsic lower bounds for efficient approximation
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
A constraint solver for software engineering : finding models and cores of large relational specifications
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-120).Relational logic is an attractive candidate for a software description language, because both the design and implementation of software often involve reasoning about relational structures: organizational hierarchies in the problem domain, architectural configurations in the high level design, or graphs and linked lists in low level code. Until recently, however, frameworks for solving relational constraints have had limited applicability. Designed to analyze small, hand-crafted models of software systems, current frameworks perform poorly on specifications that are large or that have partially known solutions. This thesis presents an efficient constraint solver for relational logic, with recent applications to design analysis, code checking, test-case generation, and declarative configuration. The solver provides analyses for both satisfiable and unsatisfiable specifications--a finite model finder for the former and a minimal unsatisfiable core extractor for the latter. It works by translating a relational problem to a boolean satisfiability problem; applying an off-the-shelf SAT solver to the resulting formula; and converting the SAT solver's output back to the relational domain. The idea of solving relational problems by reduction to SAT is not new. The core contributions of this work, instead, are new techniques for expanding the capacity and applicability of SAT-based engines. They include: a new interface to SAT that extends relational logic with a mechanism for specifying partial solutions; a new translation algorithm based on sparse matrices and auto-compacting circuits; a new symmetry detection technique that works in the presence of partial solutions; and a new core extraction algorithm that recycles inferences made at the boolean level to speed up core minimization at the specification level.by Emina Torlak.Ph.D
A Polyhedral Study of Mixed 0-1 Set
We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set
Effective algorithms and protocols for wireless networking: a topological approach
Much research has been done on wireless sensor networks. However, most protocols
and algorithms for such networks are based on the ideal model Unit Disk Graph
(UDG) model or do not assume any model. Furthermore, many results assume the
knowledge of location information of the network. In practice, sensor networks often
deviate from the UDG model significantly. It is not uncommon to observe stable long
links that are more than five times longer than unstable short links in real wireless
networks. A more general network model, the quasi unit-disk graph (quasi-UDG)
model, captures much better the characteristics of wireless networks. However, the
understanding of the properties of general quasi-UDGs has been very limited, which
is impeding the design of key network protocols and algorithms.
In this dissertation we study the properties for general wireless sensor networks
and develop new topological/geometrical techniques for wireless sensor networking.
We assume neither the ideal UDG model nor the location information of the nodes.
Instead we work on the more general quasi-UDG model and focus on figuring out
the relationship between the geometrical properties and the topological properties of
wireless sensor networks. Based on such relationships we develop algorithms that can
compute useful substructures (planar subnetworks, boundaries, etc.). We also present direct applications of the properties and substructures we constructed including routing,
data storage, topology discovery, etc.
We prove that wireless networks based on quasi-UDG model exhibit nice properties
like separabilities, existences of constant stretch backbones, etc. We develop
efficient algorithms that can obtain relatively dense planar subnetworks for wireless
sensor networks. We also present efficient routing protocols and balanced data storage
scheme that supports ranged queries.
We present algorithmic results that can also be applied to other fields (e.g., information
management). Based on divide and conquer and improved color coding
technique, we develop algorithms for path, matching and packing problem that significantly
improve previous best algorithms. We prove that it is unlikely for certain
problems in operation science and information management to have any relatively
effective algorithm or approximation algorithm for them
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