My long and pleasant interaction with computer science can be traced back to a year and a half ago, when I just started learning programming. Before I went to college, my main motivation for studying computer science was to participate in the computer Olympic competition. My achievements have won the first prize of Romanian National Olympics for many years in a row, and won international awards (including two gold medals 1 silver IOI).
In college, I naturally attracted the research of theoretical computer science. I worked in this field for three years under the guidance of Eric Des Moines. Below, I will touch on the contribution, during which I made some. My main research interests are related to complexity, concrete calculation model (lower bound) and advanced data structures and algorithms.
The research of theoretical computer science focuses on my doctoral project. After finishing my postdoctoral studies, I may want to get a position in academia. Here, I am full of energy, and my good experience in teaching, including a new postgraduate course, works as a teaching assistant at MIT.
Complexity of concrete. My most extensive contribution to the complexity of dynamic cellprobe is published in SICOMP, STOC, SODA and ICALP through a series of papers. Cell detection model is a powerful heterogeneous computing model, which is used to analyze static or dynamic data structure problems. For dynamic problems, the lower bound has been proved to use Fredman and Saks timing techniques, which can be traced back to 89 of STOC. Derived from a lower bound (LG N/LG LG N) in this file, where n is the representation of numerical problems. Although the flurry of works shows similar lower limits of various problems, there is no higher lower limit to prove that in 15, this limit is determined as the center of papers and investigations on open field problems.
We cooperate with Xikangpu, STOC and Suda Alec? Demaine appears in the file, and the lower bound of display (LG N) is used to maintain some dynamic connections, which breaks this long-standing obstacle. Our combination embodies the optimal solution of folklore (enhanced binary tree) and is a typical dynamic calculation. Despite intensive learning, there are strict restrictions even in weak algebraic models. Our proof of constrained dynamic connection includes the optimality of the dynamic graph algorithm of the famous Sleator and Tarjan's dynamic tree.
My work on these issues is recognized as the best undergraduate research computer research association award in 2004. Interestingly, our initial approach seems to be a completely different timing technology. But working with Tanit in Corina? A (Patra? Cubic meters), we found a subtle change in timing technology, which is quite. With this better understanding, we provide an optimal lower bound probe model to solve the first open problem. A survey by milt Sen shows that this is almost the second improvement. Our work won the ICALP Best Student Thesis Award.
In the recently submitted paper Mikel Thorup, we made a breakthrough in the complexity of static cell probes. Up to now, there is basically a static data structure with space-time balance proved by known technology: reducing the complexity of asymmetric communication. However, it is understood that this method cannot prove that the lower limit of superconstant is the most natural query and the parameter setting of a machine word: O(LG N) bit. In addition, communication complexity can't distinguish the space of polynomial factors and the most natural problems, among which the interesting phenomenon occurs in polynomial domain. We proved the first lower limit, broke the communication barrier, and were not subject to these restrictions. One of the basic meanings of our results is the distance between the first polynomial and a nearly linear space (arbitrary space N 1+O( 1)). Our boundary gives a complete understanding of predecessor search, which is one of the most basic and in-depth research problems. An amazing conclusion is, Fan? Underboas is a famous quasi-linear spatial data structure, which performs best in dynamic situations. Another interesting conclusion applies to the external memory model: using the classic B-tree or the best RAM based on comparison is always the best solution, while ignoring the benefits of external memory.
These results open the door to many interesting questions about the complexity of cell probes, which I intend to study. In the dynamic case, it may be necessary to prove the lower bound of multiple logarithms (for example, in continuous size range query) or N( 1) (for example, in the dynamic problem of directed graphs). In both cases, these problems have been widely studied on the upper side, but we can't hope to know the lower limit of their progress. Under static conditions, we can ask for a higher lower limit. Now, we are not limited to the complexity of communication. In particular, will it be an interesting demonstration to prove the world? Dimensional disaster? This is a crucial question to keep guessing.
Although I focus on powerful computational models, such as circuit and branch planning, such as cell probe model analysis, I still maintain an active interest. The information theory tools and intuition I used in the cell probe model will also prove to be useful, which is quite possible in other cases. For example, Adler, Des Moines and Harvey appeared in Working Together. We use tools to analyze the information transmission of the whole asymmetric channel from the complexity of communication. This problem has been widely studied and many protocols have been proposed in sensor networks. We have proved this problem, and the most famous solution is almost to use the lower limit of behavior.
Data structure and algorithm. My early computer Olympic competition training, programmers and contestants naturally made me have a strong appreciation of the algorithm. Although my work is complicated, I think I have an instinctive pattern reasoning algorithm.
One of my most influential papers was published in SICOMP and FOCS, which is a binary search tree focusing on competitiveness. The famous dynamic optimal guesses Sleator and Tarjan assert that octree is O( 1) competitive. But there is no competition for the ordinary O(LG N), which has been proved to be an eight-character tree or any other binary search tree for more than twenty years. In the joint work of Des Moines, Harmon and Iacono, we describe a new search tree that can be proved to be O(LG LG N) competition. Of course, there are two important open questions about this result: Is it an O( 1) competitive search tree? Is splay tree O(LG N) competitive?
The research of modern data structure focuses on the important field of integer search. ? Lower boas recursion is probably the most famous field, and its elegance contributes to the general field of motivation. For the predecessor's problem, the algorithm proved to be nervous about my recent work Mikel Thorup mentioned above. However, in the one-dimensional dynamic range report, the result is not the same. Working with mortensen and Pagh of STOC, we have developed a basic new recursive idea, which has produced amazing exponential improvement in query. Applicable to Terry on method of bisection Road? Opposing Andrew boas used a more complicated recursive path (similar to Van Ander's boas search itself). But the algorithm is very clean and elegant.
Recently, I am very interested in hashing and its application. The STOC file we mentioned above needs to develop an amazing hash primitive data structure, using sublinear memory (without actual memory set), so as to maintain a perfect hash function for a set of dynamic range reports.
The strict upper and lower bounds of Des Moines, Meyer ·AUF· de Hyde and Pug are in my later Latin thesis. An important factor in our development is that the dynamic dictionary uses the asymptotically optimal space compactly at the same time, which is fixed with the time of each operation with high probability. Previous dictionaries can only meet one of these requirements. Balaam and Demaine, another group of my WADS thesis, use the idea of hashing to reach the famous 3SUM problem of the first quadratic algorithm, using? Parallel? RAM or external memory mode (bits, packaged separately, larger memory page).
There are many interesting open-ended questions that I want to study. Perhaps the most fundamental thing is the representation of deterministic dictionary, which is one of the main purposes of calculating randomness. Other interesting problems include permutation hash family, which also plays an important role in cryptography. In Latin American literature, as mentioned above, we have arranged a hash function, which is not as big as k K- wise and can independently develop an interesting family, but it also has similar concentration boundaries.
I am also interested in algorithmic number theory, and there are three published results in this field. In addition, in an ongoing cooperative research project, we are looking for the problem of calculating the original lattice shape in the plane. The intersection of geometric number theory is an exciting problem, which has a long history in mathematics and can be traced back to Gauss. Our algorithm is suitable for polygons, and its speed is obviously more accurate than the previous methods. A piece of paper from R&S Corina Tarnett? A (Pettre? Cubic meters), we describe a fast algorithm for a specific triangle. we
Use this to establish the ranking of the algorithm and select the Farey sequence of the query, which is the second order of speed ratio enumeration.
Teaching. I think doing research is an indispensable part of teaching. If not, you can find a way to present it to others. This discovery is far from complete. More importantly, a large number of argumentation results are organized, and researchers must share them with teachers, because without it, researchers cannot get a clear direction, and his work is an important skill.
My early experience and students came to the Romanian National Olympic Competition and became members of the Balkan Olympic Science Committee. Yes, people are problematic, primitive and elegant, and at the same time measure the difficulty of selecting the best talented students from a group. This requires perhaps the most elusive skill. The teacher enters the students' minds and judges the difficulty within five hours according to his own ability. Although this is not a skill, I can't expect to master it completely. The results of the competition show that my question is a compliment from the members of the high-level Committee for my contribution.
My most remarkable and enjoyable teaching experience is Advanced Data Structure by Professor Erik Demaine, who is a teaching assistant of postgraduate courses. I created and graded problem sets and four lecture professors. However, the most interesting aspect is working with Eric from beginning to end? Create? This process. We must decide what should cover a wide range of topics and how to best present each topic. In such an ancient and diverse field, this is a very challenging but intellectually rewarding task. This is especially encouraging for those who claim to be impressed by the breadth and consistency of courses in other universities.
Conclusion. I look forward to continuing my doctoral research career. These are some open questions that inspire me and I will continue to work hard. In addition, this happened at MIT, and the members of the theoretical team gave me a precious opportunity to broaden my horizons and engage in many research fields at an unexpected moment. In view of my background, I believe I have the ability to make an important contribution to this cause.
Through the sharing of American computer CS professional documents, I believe that many students who intend to apply for American graduate students can refer to the above information and make preparations and plans for applying for American graduate students in advance.