A map redrawing the boundaries of City Council districts will likely advance this week. Councillors could also end up putting a final stamp of approval on the map, which moves 12 precincts in seven districts.

District 2 Councillor Bill Linehan, who chairs the Council’s redistricting committee, released his map on Monday with the aim of gaining the approval of the full 13-member council on Wednesday, Aug. 22.

Boston is required to redraw the city’s nine Council districts every 10 years, after the U.S. Census figures are released.

The figures have shown Boston’s population leapt 4.8 percent to 617,594 people. But the shift left some districts imbalanced, including Dorchester’s District 3. That forces the council’s redistricting committee to add residents to some districts and move residents out of over-populated districts, like District 2, which includes South Boston.

Councillors were split over how to solve the problem – often compared to a Rubik’s Cube – particularly if it meant dividing neighborhoods. At one point, the possibility of two councillors moving or giving up their seats was raised.

Local redistricting activists called for a total overhaul of the council districts, demanding more opportunities for candidates of color and decrying a set-up that has remained unchanged since the 1980s. Their proposed map did not appear to gain traction.

Linehan’s map includes the following proposed changes:

--District 3, represented by freshman Councillor Frank Baker, picks up the Polish Triangle (Ward 7’s Precincts 8 and 9) and loses two Lower Mills precincts (Ward 17’s Precincts 12 and 14). District 3 also gains Ward 7 Precinct 7, which includes Carson Beach, and Ward 7 Precinct 10 and Ward 13 Precinct 5.

--District 4, represented by Councillor Charles Yancey, picks up two Lower Mills precincts that Baker loses, as well as Ward 13 Precinct 4.

--The South End remains split between several Council districts, with two precincts moving into District 7, represented by Tito Jackson. District 2 adds the City Hall precinct (Ward 3 Precinct 6) while dropping the Dorchester precincts (the Polish Triangle).

--Only Districts 5 (Roslindale, Hyde Park and Mattapan) and 9 (Allston/Brighton) escaped without any changes.

“This Committee has embarked on fulfilling the goals of legal compliance, creating or preserving neighborhood unity where possible, accounting for the demographic shifts, and limiting disruption for voters,” Linehan wrote in the committee report. “The Committee fulfilled its commitment to a public process by conducting redistricting hearings throughout the neighborhoods of the City of Boston, taking testimony from an array of interested persons, and conducting several public meetings in City Hall. The attached plan embodies the fulfillment of the Committee’s redistricting goals, public comment, and Councillor concerns.’”

Councillors must send an ordinance detailing the changes to Mayor Thomas Menino’s desk in the next few months, since any person running for City Council in the 2013 elections must be living in their respective district 12 months before the election.

The full committee report is available here in PDF form. A map with the proposed changes is available here.