Zhixiang Chen, Ph.D.

Publications  

Spring 2012 Teaching  

Zhixiang received his Ph.D. in Computer Science from Boston University in January 1996. He taught at Southwest State University from Fall 1995 to September 1997. He also studied at the University of Illinois and worked and stuided at Huazhong University of Science and Technology. His research interests include Intelligent Web Search, Computational Complexity Theory, Computational Learning Theory, Informational Retrieval, Data Mining and Web Mining, Algorithms, and Bioinformatics. He has taught a wide range of computer science courses. He is the Department Chair and the Associate Director for research at the Computing and Info Tech Center (CITeC) at UTPA.

Recent Research

• Jian Tang, Zhixiang Chen, Ada Fu and David Cheung, Enhancing effectiveness of outlier detection for low density patterns, in M. Cheng, P. Yu and B. Liu (eds.), Advances in Knowledge Discovery and Data Mining (PAKDD'02), Lecture Notes in Computer Science, LNCS 2336, pp. 535-548, 2002. Springer.

  Each year the steering committee of the Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) presents an award for The Most Influential Paper. The candidates for the Most Influential Paper Award are those papers published at this conference ten years prior to the current conference. The award recognizes a paper that has had significant influence over the past decade. Google Scholar is used to identify a candidate pool of papers. These papers are then reviewed by the awards committee to consider the quality of citations. An important criterion is that the paper should present novel and big ideas which change our way of thinking. A challenger/champion approach is used by the awards committee to identify the most influential paper.

His recent research focuses on developing a theory of testing monomials in multivariate polynomials. Here is a list of his papers in this new area.

1. Zhixiang Chen, Bin Fu, Robert Schweller and Yang Liu, On Testing Monomials in Multivariate Polynomials. Journal of Theoretical Computer Science, Special Issue of the Fifth Annual International Conference on Combinatorial Optimization and Applications. Forthcoming. On-line completion: 13-APR-2012. DOI information: 10.1016/j.tcs.2012.03.038. 2012. This is an expanded version of our two COCOA'11 papers. Complexity issues about testing monomials in polynomials with negative coefficients are considered in this paper.

2. Zhixiang Chen and Bin Fu, Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials. J. Comb. Optim. Special Issue of the Fourth Annual International Conference on Combinatorial Optimization and Applications, 2010. Forthcoming. On-line completion: May-2012. DOI Information: 10.1007/s10878-012-94965. 2012. This is an expanded version of our COCOA'10 paper.

3. Zhixiang Chen and Bin Fu, The Complexity of Testing Monomials in Multivariate Polynomials, Electronic Colloquium on Computational Complexity (ECCC-TR10-114) ( link ). Also, in arXiv:1007.2673v1( link ). June 20, 2010. The extended abstract is in COCOA'2011.

   The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. The complexity aspects of this problem and its variants are investigated with two folds of objectives. One is to understand how this problem relates to critical problems in complexity, and if so to what extent. The other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems. A series of results about $\Pi\Sigma\Pi$ and $\Pi\Sigma$ polynomials are obtained in this paper, laying a basis for further study along this line.

4. Zhixiang Chen, Bin Fu, Yang Liu, and Robert Schweller, Algorithms for Testing Monomials in Multivariate Polynomials, Electronic Colloquium on Computational Complexity (ECCC-TR10-114) ( link ). Also, in arXiv:1007.2675. ( link ). July 2, 2010. The extended abstract is in COCOA'2011.

   This paper is our second step towards developing a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by an arithmetic circuit has some types of monomials in its sum-product expansion. The complexity aspects of this problem and its variants have been investigated in our first paper by Chen and Fu (2010), laying a foundation for further study. In this paper, we present two pairs of algorithms. First, we prove that there is a randomized $O^*(p^k)$ time algorithm for testing $p$-monomials in an $n$-variate polynomial of degree $k$ represented by an arithmetic circuit, while a deterministic $O^*(6.4^k + p^k)$ time algorithm is devised when the circuit is a formula, here $p$ is a given prime number. Second, we present a deterministic $O^*(2^k)$ time algorithm for testing multilinear monomials in $\Pi_m\Sigma_2\Pi_t\times \Pi_k\Pi_3$ polynomials, while a randomized $O^*(1.5^k)$ algorithm is given for these polynomials. The first algorithm extends the recent work by Koutis (2008) and Williams (2009) on testing multilinear monomials. Group algebra is exploited in the algorithm designs, in corporation with the randomized polynomial identity testing over a finite field by Agrawal and Biswas (2003), the deterministic noncommunicative polynomial identity testing by Raz and Shpilka (2005) and the perfect hashing functions by Chen {\em at el.} (2007). Finally, we prove that testing some special types of multilinear monomial is W[1]-hard, giving evidence that testing for specific monomials is not fixed-parameter tractable.

5. Zhixiang Chen and Bin Fu, Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials, Electronic Colloquium on Computational Complexity (ECCC-TR10-124) ( link ). Also, in arXiv:1007.2678. ( link ). July 15, 2010. The extended abstract is in COCOA'2010.

   This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a $\Pi\Sigma\Pi$ polynomial. We first prove that the first problem is \#P-hard and then devise a $O^*(3^ns(n))$ upper bound for this problem for any polynomial represented by an arithmetic circuit of size $s(n)$. Later, this upper bound is improved to $O^*(2^n)$ for $\Pi\Sigma\Pi$ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for $\Pi\Sigma$ polynomials. On the negative side, we prove that, even for $\Pi\Sigma\Pi$ polynomials with terms of degree $\le 2$, the first problem cannot be approximated at all for any approximation factor $\ge 1$, nor {\em "weakly approximated"} in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time $\lambda$-approximation algorithm for $\Pi\Sigma\Pi$ polynomials with terms of degrees no more a constant $\lambda \ge 2$. On the inapproximability side, we give a $n^{(1-\epsilon)/2}$ lower bound, for any $\epsilon >0,$ on the approximation factor for $\Pi\Sigma\Pi$ polynomials. When terms in these polynomials are constrained to degrees $\le 2$, we prove a $1.0476$ lower bound, assuming $P\not=NP$; and a higher $1.0604$ lower bound, assuming the Unique Games Conjecture.