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In this paper we propose and study two practical variations of the map labeling problem: Given a set S of n distinct (point) sites in the plane, label each site with: (1) a pair of non-intersecting squares of maximum possible size, (2) a pair of non-intersecting circles of maximum possible size (all the squares and circles are topologically open and are of uniform size). Almost nothing has been done before in this aspect, i.e., multi-label map labeling. We obtain constant-factor approximation algorithms for these problems. We also study bicriteria approximation schemes for these problems under a mild condition. [ABSTRACT FROM AUTHOR]

Abstract: Many students need assistance in debugging to achieve progress when they learn to write computer programs. Face‐to‐face interactions with individual students to give feedback on their programs, although definitely effective in facilitating their learning, are becoming difficult to achieve with ever‐growing class sizes. This paper proposes a novel approach to providing practical automated debugging advice to support students' learning, based on the strong relationship observed between common wrong outputs and the corresponding common bugs in students' programs. To implement the approach, we designed a generic system architecture and process, and developed a tool called Virtual Debugging Advisor (ViDA) that was put into use in classes in a university. To evaluate the effectiveness of ViDA, a controlled experiment and a survey were conducted with first year engineering students in an introductory computer programming course. Results are encouraging, showing that (a) a higher proportion of students could correct their faulty code themselves with ViDA enabled, (b) an overwhelming majority of respondents found ViDA helpful for their learning of programming, and (c) most respondents would like to keep ViDA enabled when they practice writing programs. [ABSTRACT FROM AUTHOR]