Input Format

Users are expected to provide the A, b, and c of the LP formulation to the solver. The solver takes input in the following format:

Vector b

For vector b, the input should contain the budget for each item. The representation needs to be dense: every item needs to have a budget. For input in AVRO, the schema should be as follows:

{
   "name" : "itemId",
   "type" : "int"
 }, {
   "name" : "budget",
   "type" : "double"
 }

If we are using the parallel version of DuaLip and solving many separate problems in parallel, we need to add a new field problemId (unique identifier for distinguishing a specific problem) to the schema:

{
   "name" : "itemId",
   "type" : "int"
 }, {
   "name" : "budget",
   "type" : "double"
 }, {
   "name" : "problemId",
   "type" : "long"
 }

Matrix A & c

If it is a MOO problem, we take a dense representation.

• id is a unique identifier of the block.

• a contains the dense constraints matrix A(row)(column).

• c contains a dense objective function vector.

For input in AVRO, the schema should be as follows:

{
    "name" : "id",
    "type" : [ "long" ]
  }, {
    "name" : "a",
    "type" : [ {
      "type" : "array",
      "items" : [ {
        "type" : "array",
        "items" : [ "double"]
      }]
    }]
  }, {
    "name" : "c",
    "type" : [ {
      "type" : "array",
      "items" : "double"
    }]
  }

If we are using the parallel version of MooSolver, we also need to add a new field problemId (unique identifier for distinguishing a specific problem) to the schema:

{
    "name" : "id",
    "type" : [ "long" ]
  }, {
    "name" : "a",
    "type" : [ {
      "type" : "array",
      "items" : [ {
        "type" : "array",
        "items" : [ "double"]
      }]
    }]
  }, {
    "name" : "c",
    "type" : [ {
      "type" : "array",
      "items" : "double"
    }, {
    "name" : "problemId",
    "type" : [ "long" ]
    }]
  }

If it is a Matching problem, we take a sparse representation. We keep the items in A and c which belong to same block together, to facilitate projection.

id is a unique identifier of the block, i.e. impression id for some problems. Each id corresponds to an array of tuples, which is in the format of (rowId, c(rowId), a(rowId)).

{
    "name" : "id",
    "type" : [ "string" ]
  }, {
    "name" : "data",
    "type" : [ {
      "type" : "array",
      "items" : [ {
        "type" : "record",
        "name" : "data",
        "fields" : [ {
          "name" : "rowId",
          "type" : "int"
        }, {
          "name" : "c",
          "type" : "double"
        }, {
          "name" : "a",
          "type" : "double"
        } ]
      } ]
    } ]
  }