Linear-Tree GP and Its Comparison with Other GP Structures

Abstract. In recent years different genetic programming (GP) structures have emerged. Today, the basic forms of representation for genetic programs are tree, linear and graph structures. In this contribution we introduce a new kind of GP structure which we call Linear-tree. We describe the linear-tree-structure, as well as crossover and mutation for this new GP structure in detail. We compare linear-tree programs with linear and tree programs by analyzing their structure and results on different test problems. 1 Introduction of Linear-Tree GP The representations of programs used in Genetic Programming can be classified by their underlying structure into three major groups: (1) tree-based [Koz92,Koz94], (2) linear [Nor94,BNKF98], and (3) graph-based [TV96] representations. This paper introduces a new representation for GP programs. This new representation

The Improved GP 2 Compiler

GP 2 is a rule-based programming language based on graph transformation rules which aims to facilitate program analysis and verification. Writing efficient programs in such a language is challenging because graph matching is expensive. GP 2 addresses this problem by providing rooted rules which, under mild conditions, can be matched in constant time. Recently, we implemented a number of changes to Bak's GP 2-to-C compiler in order to speed up graph programs. One key improvement is a new data structure for dynamic arrays called BigArray. This is an array of pointers to arrays of entries, successively doubling in size. To demonstrate the speed-up achievable with the new implementation, we present a reduction program for recognising binary DAGs which previously ran in quadratic time but now runs in linear time when compiled with the new compiler.Comment: 11 pages, 2020. arXiv admin note: substantial text overlap with arXiv:2002.0291

A Reference Interpreter for the Graph Programming Language GP 2

GP 2 is an experimental programming language for computing by graph transformation. An initial interpreter for GP 2, written in the functional language Haskell, provides a concise and simply structured reference implementation. Despite its simplicity, the performance of the interpreter is sufficient for the comparative investigation of a range of test programs. It also provides a platform for the development of more sophisticated implementations.Comment: In Proceedings GaM 2015, arXiv:1504.0244

Maximum Matching in Turnstile Streams

We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass $2$-approximation streaming algorithm can be easily obtained with space $O(n \log n)$, where $n$ denotes the number of vertices of the input graph. We show that no such result is possible if edge deletions are allowed, even if space $O(n^{3/2-\delta})$ is granted, for every $\delta > 0$. Specifically, for every $0 \le \epsilon \le 1$, we show that in the one-pass turnstile streaming model, in order to compute a $O(n^{\epsilon})$-approximation, space $\Omega(n^{3/2 - 4\epsilon})$ is required for constant error randomized algorithms, and, up to logarithmic factors, space $O( n^{2-2\epsilon} )$ is sufficient. Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest

Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor