17889266
Negative-Weight Cycle Algorithms
The problem of finding a negative cycle in a weighted, directed graph is discussed here. First the algorithm for printing out a negative cycle reachable from the sources, with the running time no worse than the Bellman-Ford algorithm for the single-source shortest-path problem, is presented. Then an approach with the same time complexity, which could be used for outputting a negative cycle that may not be reachable froms, is reported.
15675165
Maximum Common Subgraph: Upper Bound and Lower Bound Results
In bio informatics, the biological structure matching problems can be formulated as the problem of finding the maximum common subgraph. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest. In this paper, first we derive the lower bound result for the exact algorithms of the maximum common induced subgraph of two graphs, based on the current research progress in the area of parameterized computation. Then we investigate the upper bound and design the approaches for addressing this problem. Basically, this problem can be reduced to find a maximum clique in the product graph of the two given graphs. In consideration of the upper bound result, the obtained lower bound result is asymptotically tight. We would like to point out that our lower bound result presented here is currently best-known
2661456
Linear FPT reductions and computational lower bounds
We develop new techniques for deriving very strong computational lower bounds for a class of well-known NP-hard problems, including weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(nk) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k) no(k) for any function f, even if we restrict the parameter value k to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be Θ(μ(n)) for any reasonable function μ, no algorithm of running time no(k) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds are also derived for other problems in the above class. Our techniques can be extended to derive computational lower bounds on approximation algorithms for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/ε)no(1/ε) for any function f unless an unlikely collapse occurs in parameterized complexity theory.
10668543
Parameterized Computation of LCS for Two Sequences
The problem of finding the longest common subsequence is a well-known optimization problem because of its applications, especially in bioinformatics. In this paper, by applying the techniques developed in parameterized computation, an efficient approach for the problem of finding the longest common subsequence of two sequences is presented. The parameterized approach is compared with the well-known dynamic programming approach for the problem. The parameterized approach is much more efficient, as is shown by the experimental results.
43590220
Lower Bounds and Parameterized Approach for Longest Common Subsequence
In this paper, different parameterized versions of the longest common subsequence (LCS) problem are extensively investigated and computational lower bound results are derived based on current research progress in parameterized computation. For example, with the number of sequences as the parameter k, the problem is unlikely to be solvable in time f(k)no(k), where n is the length of each sequence and f is any recursive function. The lower bound result is asymptotically tight in consideration of the dynamic programming approach of time O(nk). Computational lower bounds for polynomial-time approximation schemes (PTAS) for the LCS problem are also derived. It is shown that the LCS problem has no PTAS of time f(1/ e)no(1/ e) for any recursive function f, unless all SNP problems are solvable in subexponential time. Compared with former results on this problem, this result has its significance. Finally a parameterized approach for the LCS problem is discussed, which is more efficient than the dynamic programming approach, especially when applied to large scale sequences.
2218327
Strong computational lower bounds via parameterized complexity
We develop new techniques for deriving strong computational lower bounds for a class of well-known NP-hard problems. This class includes weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(n^k) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k)n^o^(^k^) for any function f, even if we restrict the parameter values to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be of the order @Q(@m(n)) for any reasonable function @m, no algorithm of running time n^o^(^k^) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds on the computational complexity are also derived for other NP-hard problems in the above class. Our techniques can be further extended to derive computational lower bounds on polynomial time approximation schemes for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/@e)n^o^(^1^/^@e^) for any function f unless an unlikely collapse occurs in parameterized complexity theory.
21231697
Finding and Analyzing Database User Sessions
A database user session is a sequence of queries issued by a user (or an application) to achieve a certain task. Analysis of task-oriented database user sessions provides useful insight into the query behavior of database users. In this paper, we describe novel algorithms for identifying sessions from database traces and for grouping the sessions different classes. We also present experimental results.
12511265
A Scalable Algorithm for Adjusting Node-Node Overlaps
The node-node overlaps, which occur in drawing of labeled graphs, and more importantly, in the dynamic drawing, have been a problem in graph visualization. Several approaches have recently been proposed to solve such a problem. These approaches, however, lack the scalabilities of dealing with large number of overlapping nodes. Providing a formal description of the problem, this paper presents a scalable version of our previous approach called the force-transfer algorithm. Compared to other methods, our new algorithm is able to achieve the compact adjusted layout of a large graph
18862916
Clustering graphs for visualization via node similarities
Graph visualization is commonly used to visually model relations in many areas. Examples include Web sites, CASE tools, and knowledge representation. When the amount of information in these graphs becomes too large, users, however, cannot perceive all elements at the same time. A clustered graph can greatly reduce visual complexity by temporarily replacing a set of nodes in clusters with abstract nodes. This paper proposes a new approach to clustering graphs. The approach constructs the node similarity matrix of a graph that is derived from a novel metric of node similarity. The linkage pattern of the graph is thus encoded into the similarity matrix, and then one obtains the hierarchical abstraction of densely linked subgraphs by applying the k-means algorithm to the matrix. A heuristic method is developed to overcome the inherent drawbacks of the k-means algorithm. For clustered graphs we present a multilevel multi-window approach to hierarchically drawing them in different abstract level views with the purpose of improving their readability. The proposed approaches demonstrate good results in our experiments. As application examples, visualization of part of Java class diagrams and Web graphs are provided. We also conducted usability experiments on our algorithm and approach. The results have shown that the hierarchically clustered graph used in our system can improve user performance for certain types of tasks.
9414412
Concept-based biomedical text retrieval
One challenging problem for biomedical text retrieval is to find accurate synonyms or name variants for biomedical entities. In this paper, we propose a new concept-based approach to tackle this problem. In this approach, a set of concepts instead of keywords will be extracted from a query first. Then these concepts will be used for retrieval purpose. The experiment results show that the proposed approach can boost the retrieval performance and it generates very good results on 2005 TREC Genomics data sets.
5775998
Identification of clusters in the Web graph based on link topology
The Web graph has recently been used to model the link structure of the Web. The studies of such graphs can yield valuable insights into Web algorithms for crawling, searching and discovery of Web communities. This paper proposes a new approach to clustering the Web graph. The proposed algorithm identifies a small subset of the graph as "core" members of clusters, and then incrementally constructs the clusters by a selection criterion. Two qualitative criteria are proposed to measure the quality of graph clustering. We have implemented our algorithm and tested a set of arbitrary graphs with good results. Applications of our approach include graph drawing and Web visualization.