# A 3/4-Approximation Algorithm for Multiple Subset Sum by Ageev A.A., Baburin A.E., Gimandi E.K.

By Ageev A.A., Baburin A.E., Gimandi E.K.

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Similar to (Buneman et al. 2 Operators m1 m2 ORDER ODate CName CAddr m PO ORDER Amount OrderDate OrderDate CAddr Amount CUST CUST Customer x1 y2 x3 y2 priority order for conflict resolution heuristic: z y1 x2 x Customer y x z1 + z1 x o x3 È o y1 + y2 39 z o + z1 +-,-+ y2 x +- z1 -o +o x3 oo o+ o+o -o ++ +-+ -- z o+ y1 Fig. 4. Merging two sample schemas ger and Bernstein 2003), the algorithm consists of three conceptual steps: node renaming, graph union, and conﬂict resolution. 1. In the ﬁrst step, the graph nodes at the blunt ends of map are renamed to their targets at sharp ends, in both graphs m1 and m2 .

Operator DeleteHard(M , selector, dep) toDelete = selector + Reachable(selector, Invert(dep)); toKeep = All(M ) − toDelete; return ExtractMin(M , toKeep, dep); Essentially, the operator DeleteHard takes All(M ) elements of M , subtracts from this set the elements to be deleted, and applies ExtractMin to extract the unselected portion of the model. , elements that are existentially dependent on the elements to be deleted. Such would-be dangling elements are obtained by passing the selector and the inverted dependency morphism to the operator Reachable.

The literals include strings, integers, ﬂoats, and other data types. The type of attribute O is deﬁned as a union type of OIDs and literals. CREATE TABLE PRODUCTS ( PID int PRIMARY KEY, PName varchar ) Table type column:1 Column type a2 a1 name column:2 PRODUCTS type SQLtype int name PID SQLtype varchar name PName a3 keyCol a4 type PrimaryKey S a1 a1 a1 a1 a2 a2 a2 a3 a3 a3 a4 a4 P O N Table type a2 column 1 column a3 2 name “PRODUCTS” type Column SQLtype int name “PID” type Column SQLType varchar name “PName” type PrimaryKey keyCol a2 Fig.