import ProposalMatchConfig
-data Real wt => Instance wt = Instance Int Int (Int -> Int -> wt)
+data Instance = Instance
+ Int -- numReviewers
+ Int -- numProposals
+ (Int -> Wt) -- reviewer -> relative load
+ (Int -> Int -> Wt) -- reviewer -> proposal -> pref
-doReduction :: Real wt => Instance wt -> (Int -> Int) -> Gr () wt
-doReduction (Instance numRvrs numProps prefF) expertCapF =
+prefBoringness p = if prefIsVeryBoring p then 2
+ else if prefIsBoring p then 1 else 0
+prefExpertness p = if prefIsExpert p then 2
+ else if prefIsKnowledgeable p then 1 else 0
+
+doReduction :: Instance -> Gr () Wt
+doReduction (Instance numRvrs numProps rloadF prefF) =
let
source = 0
sink = 1
- rvrNode i = 2 + i
- propNode j isExpert = 2 + numRvrs + 2*j + (if isExpert then 1 else 0)
- numNodes = 2 + numRvrs + 2*numProps
- theNodes = [(x, ()) | x <- [0 .. numNodes - 1]]
+ rvrNode i boringness = 2 + 3*i + boringness
+ propNode j expertness = 2 + 3*numRvrs + 3*j + expertness
+ numNodes = 2 + 3*numRvrs + 3*numProps
in
let
- loadEdges = do
+ totalReviews = reviewsEachProposal * numProps
+ totalRelativeLoad = foldl (+) 0 (map rloadF [0 .. numRvrs - 1])
+ targetLoad i = ceiling (numAsWt totalReviews * rloadF i / totalRelativeLoad)
+ -- A...H refer to idea book p.429
+ edgesABC = do
i <- [0 .. numRvrs - 1]
- l <- [1 .. maxReviewerLoad]
- return (source, rvrNode i, marginalLoadCost l)
- prefEdges = do
+ let tl = targetLoad i
+ l <- [0 .. tl + loadTolerance - 1]
+ let costA = if l < tl
+ then 0
+ else marginalLoadCost ((numAsWt (l - tl) + 1/2) / numAsWt loadTolerance)
+ let edgeA = (source, rvrNode i 0, costA)
+ let costB = marginalBoringCost ((numAsWt l + 1/2) / numAsWt tl)
+ let edgeB = (rvrNode i 0, rvrNode i 1, costB)
+ let costC = marginalVeryBoringCost ((numAsWt l + 1/2) / numAsWt tl)
+ let edgeC = (rvrNode i 1, rvrNode i 2, costC)
+ [edgeA, edgeB, edgeC]
+ edgesD = do
i <- [0 .. numRvrs - 1]
j <- [0 .. numProps - 1]
let pref = prefF i j
if prefIsConflict pref
- then fail "Conflict of interest"
- else return (rvrNode i, propNode j (prefIsExpert pref),
- prefToCost pref)
- wantEdges = do
+ then []
+ else [(rvrNode i (prefBoringness pref),
+ propNode j (prefExpertness pref),
+ assignmentCost pref)]
+ edgesE = do
+ j <- [0 .. numProps - 1]
+ [(propNode j 2, propNode j 0, -expertBonus)]
+ edgesFGH = do
j <- [0 .. numProps - 1]
- let wExpert = expertCapF j
- -- Yuck, too many kinds of integers.
- let wGeneral = fromInteger wantGeneralReviews +
- fromInteger wantReviewsSubstForExpert *
- (fromInteger wantExpertReviews - wExpert)
- let expertEdges = replicate wExpert (propNode j True, sink, 0)
- let rolloverEdges = replicate wGeneral (propNode j True, propNode j False, 0)
- let generalEdges = replicate wGeneral (propNode j False, sink, 0)
- expertEdges ++ rolloverEdges ++ generalEdges
- theEdges = loadEdges ++ prefEdges ++ wantEdges
+ l <- [0 .. reviewsEachProposal - 1]
+ let edgeF = (propNode j 2, propNode j 1, 0)
+ let edgeG = (propNode j 1, propNode j 0,
+ if l == 0 then -knowledgeableBonus else 0)
+ let edgeH = (propNode j 0, sink, 0)
+ [edgeF, edgeG, edgeH]
+ theNodes = [(x, ()) | x <- [0 .. numNodes - 1]]
+ theEdges = edgesABC ++ edgesD ++ edgesE ++ edgesFGH
in
mkGraph theNodes theEdges
todo = undefined
-- Returns a list of reviews as ordered pairs (reviewer#, proposal#).
-doMatching :: Real wt => Instance wt -> [(Int, Int)]
-doMatching inst@(Instance numRvrs numProps prefF) =
+doMatching :: Instance -> [(Int, Int)]
+doMatching inst@(Instance numRvrs numProps rloadF prefF) =
-- Copied from doReduction. There should be a better way to get these here.
let
source = 0
sink = 1
- rvrNode i = 2 + i
- propNode j isExpert = 2 + numRvrs + 2*j + (if isExpert then 1 else 0)
- idPropNode n = (n - (2 + numRvrs)) `div` 2
- numNodes = 2 + numRvrs + 2*numProps
+ rvrNode i boringness = 2 + 3*i + boringness
+ propNode j expertness = 2 + 3*numRvrs + 3*j + expertness
+ firstPropNode = propNode 0 0
+ idPropNode n = (n - (2 + 3*numRvrs)) `div` 3
+ numNodes = 2 + 3*numRvrs + 3*numProps
in
- let graph1 = doReduction inst (const (fromInteger wantExpertReviews)) in
+ let graph1 = doReduction inst in
let flow1 = flowDiff graph1 (snd (umcf source sink graph1)) in
- let expertCapF j = min (fromInteger wantExpertReviews) (outdeg flow1 (propNode j True)) in
- let graph2 = doReduction inst expertCapF in
- let flow2 = flowDiff graph2 (snd (umcf source sink graph2)) in
let pairs = do
i <- [0 .. numRvrs - 1]
- map (\n -> (i, idPropNode n)) (suc flow2 (rvrNode i)) in
+ boringness <- [0, 1, 2]
+ n <- suc flow1 (rvrNode i boringness)
+ if n >= firstPropNode
+ then [(i, idPropNode n)]
+ else []
+ in
sort pairs -- for prettiness
module ProposalMatchConfig where
+type Pref = Int
+type Wt = Double -- must implement RealFrac
+
+numAsWt x = fromInteger (toInteger x) :: Wt
+
+reviewsEachProposal = 3 :: Int
+
prefIsExpert p = p <= 10
+prefIsKnowledgeable p = p <= 20
+
+prefIsBoring p = p > 15
+prefIsVeryBoring p = p > 25
+
prefIsConflict p = p >= 40
-{-
-Each proposal should have 'wantExpertReviews' expert reviews plus
-'wantGeneralReviews' general reviews (can be by experts). If we
-fall short on expert reviews, we give 'wantReviewsSubstForExpert'
-additional general reviews for each expert review we fell short.
-Values 2, 1, 2 give the ">= 3 of which >= 1 is expert, failing that >= 4"
-criterion that Samir indicated.
--}
-wantGeneralReviews = 2
-wantExpertReviews = 1
-wantReviewsSubstForExpert = 2
-
--- A hard limit that we hope will never be hit.
-maxReviewerLoad = 10
+-- For now this is absolute. Later it might be proportional to a reviewer's
+-- target load.
+loadTolerance = 1 :: Int
+-- Cost to overload by one review.
+-- tx = 0 at target load, 1 at end of tolerance.
+marginalLoadCost tx = 1000 + tx*1000 :: Wt
+
+-- Cost to review a boring (or very boring) proposal.
+-- lx = 0 at no load, 1 at target load.
+marginalBoringCost lx = 1000 + lx*1000 :: Wt
+-- Additional cost to review a very boring proposal.
+marginalVeryBoringCost lx = 1000 + lx*1000 :: Wt
+
+-- Cost to make a review.
-- I'm using quadratic cost functions as a first attempt.
-prefToCost p = p ^ 2
-{-
-I chose the number 225 to make the preference difference between 20 and 25
-approximately equivalent to one unit of load imbalance (e.g., the difference
-between (k, k) and (k+1, k-1)); that seemed reasonable to me.
-Adjust the number as necessary.
--}
-marginalLoadCost nr = 225 * fromInteger nr
+assignmentCost pref = (numAsWt 10 + pref) ^ 2 :: Wt
+
+-- Bonus for a first knowledgeable or expert review.
+knowledgeableBonus = 1000 :: Wt
+
+-- Bonus for an additional expert review.
+expertBonus = 1000 :: Wt
import Data.Graph.Inductive.Graph
import Data.Graph.Inductive.Tree
+-- So we can call graphviz' at the GHCi prompt
+import Data.Graph.Inductive.Graphviz
+graphviz' g = Data.Graph.Inductive.Graphviz.graphviz' g
+
myGraph = mkGraph [(0, ()), (1, ()), (2, ())]
[(0, 1, 2), (0, 2, 3), (2, 1, -2)] :: Gr () Double
]
myPrefs = \i j -> myPrefsArray ! (i, j)
-myInst = Instance myNumRvrs myNumProps myPrefs
+myInst = Instance myNumRvrs myNumProps (const 1) myPrefs
---rdnGraph = doReduction myInst (const (fromInteger wantExpertReviews))
---(rdnFlowVal, rdnFlowResid) = umcf 0 1 rdnGraph
---rdnFlow = flowDiff rdnGraph rdnFlowResid
+rdnGraph = doReduction myInst
+(rdnFlowVal, rdnFlowResid) = umcf 0 1 rdnGraph
+rdnFlow = flowDiff rdnGraph rdnFlowResid
myMatching = doMatching myInst