Efficient Extraction of Multiple Kuratowski Subdivisions (TR)
نویسندگان
چکیده
A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdivisions to generate cut constraints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation.
منابع مشابه
Independent paths and K5-subdivisions
A well known theorem of Kuratowski states that a graph is planar iff it contains no subdivision of K5 or K3,3. Seymour conjectured in 1977 that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove several results about independent paths (no vertex of a path is internal to another), which are then used to prove Seymour’s conjecture for two classes of graphs. Th...
متن کاملDetection of Chlamydia trachomatis-DNA in synovial fluid: evaluation of the sensitivity of different DNA extraction methods and amplification systems
INTRODUCTION Polymerase chain reaction (PCR) and ligase chain reaction (LCR) are used in research for detection of Chlamydia trachomatis (C. tr.) in synovial fluid (SF). However there is no standardized system for diagnostic use in clinical practice, therefore this study aimed at determining the molecular biology method best suited to detect C. tr. from SF. METHODS SF samples were spiked with...
متن کاملSelective Tone Reservation Method for PAPR Reduction of Spatially Multiplexed OFDM Systems
Tone Reservation (TR) is one of the well-known methods for PAPR reduction of Orthogonal Frequency Division Multiplexing (OFDM) systems. In this method some sub-carriers are reserved for PAPR reduction and the symbols in these sub-carriers are selected such that the PAPR of the OFDM frame is minimized. In this paper, the iterative algorithm introduced earlier for TR method in single antenna OFDM...
متن کاملبهینه سازی مشخصه فیزیکی تالاب پیش ساخته به کمک مدل شبیهساز-بهینهساز MUSIC-GA
Nowadays, urbanization is a common process which replaces vegetation cover with impervious areas. This process increases urban stormwater. A new tendency in urban stormwater management endorses ‘source control’, whereby distributed water sensitive urban design systems are built throughout the subdivisions to alleviate the effects of land use changes. Various costs and functions are ...
متن کاملAutomatic Object Extraction from Full Differential Morphological Profile in Urban Imagery for Efficient Object Indexing and Retrievals
The differential morphological profile (DMP) can be used for automated extraction of multi-scale urban features, such as buildings, shadows, roads, and other man-made objects. However, characterization of urban features using the DMP is complicated by the fact that some objects will have response at multiple-scales within the DMP. This makes robust and efficient object indexing and retrieval di...
متن کامل