A 7/3-Approximation Algorithm for Fitting Points on the Real Line and its Application to RH Mapping
نویسندگان
چکیده
Physical mapping is an important problem in computational biology. Physical mapping is used in largescale sequencing of DNA as well as for locating genes. We study the Radiation Hybrid (RH) problem, i.e., the algorithmic part of a physical mapping method called RH mapping. In order to obtain an algorithm for the RH problem, we consider the MATRIX-TO-LINE problem, which is of obvious independent interest. We show that it can be approximated within 7=3, but not within 4=3. The goal in RH mapping is to infer the order of and distances between nmarkers on a genome. We give the first algorithm with a guaranteed convergence for the general RH problem. The RH problem can be seen as a learning problem; by our result, it can be PAC-learned.
منابع مشابه
Fitting Points on the Real Line and Its Application to RH Mapping
The Matrix-To-Line problem is that of, given an n × n symmetric matrix D, finding an arrangement of n points on the real line such that the so obtained distances agree as well as possible with the by D specified distances, w.r.t. the max-norm. The Matrix-To-Line problem has previously been shown to be NP-complete [11]. We show that it can be approximated within 2, but not within 7/5−δ for any δ...
متن کاملApproximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces
This paper introduces an implicit scheme for a continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup. The main result is to prove the strong convergence of the proposed implicit scheme to the unique solutio...
متن کاملMinimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs
This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...
متن کاملمدلسازی صفحه‌ای محیط‌های داخلی با استفاده از تصاویر RGB-D
In robotic applications and especially 3D map generation of indoor environments, analyzing RGB-D images have become a key problem. The mapping problem is one of the most important problems in creating autonomous mobile robots. Autonomous mobile robots are used in mine excavation, rescue missions in collapsed buildings and even planets’ exploration. Furthermore, indoor mapping is beneficial in f...
متن کاملThe Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007