The height of multiple edge plane trees

Multi-edge trees as introduced in a recent paper of Dziemia\'nczuk are plane trees where multiple edges are allowed. We first show that $d$-ary multi-edge trees where the out-degrees are bounded by $d$ are in bijection with classical $d$-ary trees. This allows us to analyse parameters such as the height. The main part of this paper is concerned with multi-edge trees counted by their number of edges. The distribution of the number of vertices as well as the height are analysed asymptotically

On Greedy Algorithms for Binary de Bruijn Sequences

We propose a general greedy algorithm for binary de Bruijn sequences, called Generalized Prefer-Opposite (GPO) Algorithm, and its modifications. By identifying specific feedback functions and initial states, we demonstrate that most previously-known greedy algorithms that generate binary de Bruijn sequences are particular cases of our new algorithm

DeltaTree: A Practical Locality-aware Concurrent Search Tree

As other fundamental programming abstractions in energy-efficient computing, search trees are expected to support both high parallelism and data locality. However, existing highly-concurrent search trees such as red-black trees and AVL trees do not consider data locality while existing locality-aware search trees such as those based on the van Emde Boas layout (vEB-based trees), poorly support concurrent (update) operations. This paper presents DeltaTree, a practical locality-aware concurrent search tree that combines both locality-optimisation techniques from vEB-based trees and concurrency-optimisation techniques from non-blocking highly-concurrent search trees. DeltaTree is a $k$-ary leaf-oriented tree of DeltaNodes in which each DeltaNode is a size-fixed tree-container with the van Emde Boas layout. The expected memory transfer costs of DeltaTree's Search, Insert, and Delete operations are $O(\log_B N)$, where $N, B$ are the tree size and the unknown memory block size in the ideal cache model, respectively. DeltaTree's Search operation is wait-free, providing prioritised lanes for Search operations, the dominant operation in search trees. Its Insert and {\em Delete} operations are non-blocking to other Search, Insert, and Delete operations, but they may be occasionally blocked by maintenance operations that are sometimes triggered to keep DeltaTree in good shape. Our experimental evaluation using the latest implementation of AVL, red-black, and speculation friendly trees from the Synchrobench benchmark has shown that DeltaTree is up to 5 times faster than all of the three concurrent search trees for searching operations and up to 1.6 times faster for update operations when the update contention is not too high

Broadcasting in Prefix Space: P2P Data Dissemination with Predictable Performance

A broadcast mode may augment peer-to-peer overlay networks with an efficient, scalable data replication function, but may also give rise to a virtual link layer in VPN-type solutions. We introduce a simple broadcasting mechanism that operates in the prefix space of distributed hash tables without signaling. This paper concentrates on the performance analysis of the prefix flooding scheme. Starting from simple models of recursive $k$-ary trees, we analytically derive distributions of hop counts and the replication load. Extensive simulation results are presented further on, based on an implementation within the OverSim framework. Comparisons are drawn to Scribe, taken as a general reference model for group communication according to the shared, rendezvous-point-centered distribution paradigm. The prefix flooding scheme thereby confirmed its widely predictable performance and consistently outperformed Scribe in all metrics. Reverse path selection in overlays is identified as a major cause of performance degradation.Comment: final version for ICIW'0

Rates of DNA Sequence Profiles for Practical Values of Read Lengths

A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $\ell$, and word length $n$.Consequently, we demonstrate that for $q\ge 2$ and $n\le q^{\ell/2-1}$, the number of profile vectors is at least $q^{\kappa n}$ with $\kappa$ very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors

Tree-formed Verification Data for Trusted Platforms

The establishment of trust relationships to a computing platform relies on validation processes. Validation allows an external entity to build trust in the expected behaviour of the platform based on provided evidence of the platform's configuration. In a process like remote attestation, the 'trusted' platform submits verification data created during a start up process. These data consist of hardware-protected values of platform configuration registers, containing nested measurement values, e.g., hash values, of loaded or started components. Commonly, the register values are created in linear order by a hardware-secured operation. Fine-grained diagnosis of components, based on the linear order of verification data and associated measurement logs, is not optimal. We propose a method to use tree-formed verification data to validate a platform. Component measurement values represent leaves, and protected registers represent roots of a hash tree. We describe the basic mechanism of validating a platform using tree-formed measurement logs and root registers and show an logarithmic speed-up for the search of faults. Secure creation of a tree is possible using a limited number of hardware-protected registers and a single protected operation. In this way, the security of tree-formed verification data is maintained.Comment: 15 pages, 11 figures, v3: Reference added, v4: Revised, accepted for publication in Computers and Securit