After families submit their kindergarten applications, ranking as many school choices as they like across the city, a computer algorithm makes assignments. Those from neighborhoods where students have scored low on state tests get first dibs at their top-ranked programs. Each child gets an address-based priority at one school, but it is considered only after those with test-score priority are offered seats.

The district had previously used busing to try to desegregate schools, under a 1983 agreement with the N.A.A.C.P. But a group of Chinese-American families sued in the 1990s, saying their children were being denied seats at elite campuses. The city settled the case by devising a choice-based enrollment process meant to be race-neutral but still achieve integration.

Research shows that desegregation can drive learning gains for students of all races. And on paper, San Francisco’s system showed promise. In recent years, it succeeded in breaking up racial concentrations at a handful of schools.

But over all, many parents and city leaders consider it a disappointment. The district’s schools were more racially segregated in 2015 than they were in 1990, even though the city’s neighborhoods have become more integrated, research shows. That pattern holds true in many of the nation’s largest cities, according to an analysis by Ryan W. Coughlan, an assistant professor of sociology at Guttman Community College in New York.

Segregation looks different in San Francisco than in other parts of the country. The district is one of the most diverse in the nation: 35 percent of students are Asian, 27 percent are Hispanic, 15 percent are white and 7 percent are African-American. Schools here are not racially monolithic. But over the past several decades, white, Asian and Hispanic students, on average, have been clustered in schools with more children of their own races.

While black children were slightly less racially isolated in 2015 than in 1990, that was largely a result of their lower enrollment in the district, Professor Coughlan said — a change driven by astronomical housing costs.