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A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We propose two new methods, one based on a discrete form of gradient descent, the other on simulated annealing, and report on a series of empirical tests comparing these and the other known algorithms for the problem. Based on this study, the first to be conducted, we identify the best approaches as a function of available computation time.

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BACKGROUND The development of nasopharyngeal carcinoma reflects interactions of genetics, diet, and viral agents. It is more common in Asians than non‐Asians, with different characteristic histologic types. This study examined nasopharyngeal carcinoma in the U.S. as a function of patient origin and histology. METHODS The data were from the National Cancer Data Base (NCDB). The 5069 nasopharyngeal carcinoma cases were grouped by histologic type: keratinizing squamous cell, nonkeratinizing, and undifferentiated carcinoma. Patient origin was derived from race, Hispanic ethnicity, and place of birth. RESULTS World Health Organization (WHO) type 1 keratinizing squamous cell carcinomas comprised 75% of the U.S. nasopharyngeal carcinoma cases and were found most often in U.S.‐born, non‐Hispanic whites. WHO‐ 2 nonkeratinizing and WHO‐ 3 undifferentiated carcinomas of the nasopharnyx comprised the remaining 25% of nasopharyngeal carcinomas and were more common in Asians. Histologic composition varied for each of the 12 patient origin groups in the study and correlated with survival after treatment with ionizing radiation. Asians had the highest proportion of radioresponsive WHO‐ 2 nonkeratinizing and WHO‐ 3 undifferentiated carcinomas of the nasopharynx and better survival than African‐Americans and Hispanic and non‐Hispanic whites, who had the greatest number of the less radioresponsive keratinizing squamous cell carcinomas of the nasopharynx. The 5‐year relative survival was 65% for the nonkeratinizing and undifferentiated carcinomas of the nasopharynx and 37% for the keratinizing variety. CONCLUSIONS The survival rate of the patient origin groups correlated with the histologic composition of their nasopharyngeal carcinomas. Those with the highest proportion of radioresponsive nonkeratinizing and undifferentiated carcinomas had the best survival. Cancer 1998;83:582‐588. © 1998 American Cancer Society.

Significant improvement in DSS was seen in patients with clear margins, early stage grouping and clinical (pretreatment) tumor stage, and negative nodes. Significant decrease in DSS was seen in patients with close or involved margins, advanced stage grouping and clinical (pretreatment) tumor staging, positive clinical (pretreatment) node staging, and tumor recurrence. Obtaining clear margins of resection is crucial because it significantly affects survival. A minimum of 5 years of close monitoring is recommended because of the high incidence of second primary cancers.