Tree Drawings have been used extensively in software engineering and many other business and computer applications. The basic structure of a tree allows for the organization and representation of complex information. Many commercial tools allow their users to draw or construct trees to represent a problem and/or its solution. Our focus is on dynamic trees - trees subject to frequent changes and redisplay in highly user-friendly interactive computer applications. Tree presentations in such interactive tools have to be precise and maintainable, which means, the tree presentations should maintain a particular structure so that user's mental perception of the tree is not disrupted or changed drastically when modifications are made to the tree being manipulated. Minimal modifications to the tree should cause correspondingly minimal changes to the general layout of the tree drawing and such changes should be consistent with the original layout to enable the user to anticipate them and verify their correctness with minimal mental effort. Also, display properties, like Vext, Hext, aspect ratio and space utilization efficiency of the layout are important to the user as they influence efficient use of available drawing/visualizing space which in turn affects comprehensibility of the tree drawing in question. In this thesis report, we analyze and compare three published algorithms, proposed by Workman-Bernard[1], S. Moen[3], and R. Cohen [2],to interactively manage the layout of graphically represented dynamic trees. We attempt to measure and analyze the performance of these algorithms based on their layout properties and their computational requirements. This research concludes that the Workman-Bernard (WB) algorithm when compared with its closest equivalent, Moen's algorithm, produces trees with better layout at a significantly lower computation cost.

Šiame darbe, remiantis radialiniu medžių vaizdavimu, Maple programos aplinkoje buvo realizuotas algoritmas, skirtas numeruotųjų medžių vizualizacijai plokštumoje. Po to, atsitiktinai generuojant tūkstančius įvairios eilės medžių, empiriškai nustatyta, jog ne visais atvejais tenkinami estetiniai reikalavimai. Iškilusi problema spręsta įvedant papildomus parametrus, suteikiančius medžiui lankstumo, ilgiausius takus vaizduojant vienoje iš koncentrinių elipsių, medį „užtempiant“ ant erdvinių spiralinių paviršių. Taigi mes apibendrinome radialino medžių vaizdavimo algoritmą; pasiūlėme medžio centro paieškos metodą taikyti ilgiausių takų radimui; sukūrėme iki šiol neaprašytą laurų vainiko algoritmą, skirtą vaizduoti įvairiems medžiams plokštumoje; patogumo dėlei pritaikėme Priuferio sugalvotą kodą medžiams generuoti bei išvesti apibrėžto medžio Priuferio kodą; modifikuodami radialinį medžių vizualizacijos algoritmą pavaizdavome medžius koncentrinių elipsoidų sistemoje. Darbe pasiūlyta originali idėja vizualizuoti paiešką į plotį ir į gylį įterpiant papildomas procedūras, tam tikruose algoritmo realizacijos etapuose vaizduojančias grafus bei keičiančias jų briaunų ir viršūnių spalvas. / In this paper, referring to radial tree drawing, through the medium of Maple program, an algorithm has been realized. It was meant to carry out the visualization of rooted trees on a plane. After that, randomly generating thousands of trees of a different order, it has been empirically identified that aesthetic requirements are not suitable in all cases. The arisen problem has been tackled by introducing additional parameters: they have added flexibility to trees, the longest paths representing in one of the concentric ellipsis, pulling the tree on dimensional spiral surfaces. So we have summarized the algorithm of radial tree drawing, we have suggested to apply the method of finding the tree centre in identifying the longest trails. We have created a not described yet method of the algorithm of the laurel wreath, which is meant for portraying various trees on a plane. For ease of application we have also adjusted the code introduced by Prüfer: it is meant for generating trees and for deducing Prüfer‘s code of a determined tree. By modifying the algorithm of radial tree drawing, we have pictured the trees in a system of concentric ellipsoids. The paper suggests an original idea to visualize the breadth first search and the depth first search by inserting additional procedures, showing graphs and changing the colors of their edges and summits at certain stages of the realization of the algorithm.