diff --git a/quad/ocm-typed.rkt b/quad/ocm-typed.rkt
index 9d180312..176ad7e4 100644
--- a/quad/ocm-typed.rkt
+++ b/quad/ocm-typed.rkt
@@ -1,6 +1,7 @@
 #lang typed/racket/base
 (require (for-syntax racket/base racket/syntax))
-(require racket/list sugar/debug rackunit racket/function racket/vector sugar/cache "logger-typed.rkt")
+(require/typed sugar/cache [make-caching-proc (Procedure . -> . Procedure)])
+(require racket/list sugar/debug rackunit racket/function racket/vector  "logger-typed.rkt")
 (define-logger ocm)
 
 #|
@@ -21,15 +22,360 @@ D. Eppstein, March 2002, significantly revised August 2005
 
 ;(provide smawky? make-ocm reduce reduce2 (prefix-out ocm- (combine-out min-value min-index)))
 
+(: select-elements ((Listof Any) (Listof Index-Type) . -> . (Listof Any)))
 (define (select-elements xs is)
-  (map (curry list-ref xs) is))
+  (map (λ([i : Index-Type]) ((inst list-ref Any) xs i)) is))
 
+(: odd-elements ((Listof Any) . -> . (Listof Any)))
 (define (odd-elements xs)
   (select-elements xs (range 1 (length xs) 2)))
 
+(: vector-odd-elements ((Vectorof Any) . -> . (Vectorof Any)))
 (define (vector-odd-elements xs)
   (for/vector ([i (in-range (vector-length xs))] #:when (odd? i))
     (vector-ref xs i)))
 
+(: even-elements ((Listof Any) . -> . (Listof Any)))
 (define (even-elements xs)
   (select-elements xs (range 0 (length xs) 2)))
+
+
+;; Wrapper for the matrix procedure
+;; that automatically maintains a hash cache of previously-calculated values
+;; because the minima operations tend to hit the same values.
+;; Assuming here that (matrix i j) is invariant
+;; and that the matrix function is more expensive than the cache lookup.
+
+
+(define-syntax-rule (vector-append-item xs value)
+  (vector-append xs (vector value)))
+
+(define-syntax-rule (vector-set vec idx val)
+  (begin
+    (vector-set! vec idx val)
+    vec))
+
+(define-syntax-rule (vector-cdr vec)
+  (vector-drop vec 1))
+
+(define-syntax-rule (vector-empty? vec)
+  (= 0 (vector-length vec)))
+
+
+(define (integers? x) (and (list? x) (andmap integer? x)))
+
+;; Reduce phase: make number of rows at most equal to number of cols
+(: reduce ((Vectorof Index-Type) (Vectorof Index-Type) Matrix-Proc-Type Entry->Value-Type . -> . (Vectorof Index-Type)))
+(define (reduce row-indices col-indices matrix-proc entry->value)
+  ;(vector? vector? procedure? procedure? . -> . vector?)
+  (log-ocm-debug "starting reduce phase with")
+  (log-ocm-debug "row-indices = ~a" row-indices)
+  (log-ocm-debug "col-indices = ~a" col-indices)
+  
+  (: process-stack ((Vectorof Index-Type) Index-Type . -> . (Vectorof Index-Type)))
+  (define (process-stack stack row-idx)
+    (log-ocm-debug "row stack = ~a" stack)
+    (let ([last-stack-idx (sub1 (vector-length stack))])
+      (cond
+        [(and (>= (vector-length stack) 1) 
+              (log-ocm-debug "comparing row values at column ~a" (vector-ref col-indices last-stack-idx))
+              (log-ocm-debug "end of row stack (~a) value at column ~a = ~a" (vector-ref stack last-stack-idx) (vector-ref col-indices last-stack-idx) (entry->value (matrix-proc (vector-ref stack last-stack-idx) (vector-ref col-indices last-stack-idx))))
+              (log-ocm-debug "challenger row (~a) value at column ~a = ~a" row-idx (vector-ref col-indices last-stack-idx) (entry->value (matrix-proc row-idx (vector-ref col-indices last-stack-idx))))
+              (> (entry->value (matrix-proc (vector-ref stack last-stack-idx) (vector-ref col-indices last-stack-idx)))
+                 (entry->value (matrix-proc row-idx (vector-ref col-indices last-stack-idx)))))
+         
+         (log-ocm-debug "challenger row (~a) wins with a new minimum ~a, so end of row stack (~a) is removed" row-idx (entry->value (matrix-proc row-idx (vector-ref col-indices last-stack-idx))) (vector-ref stack last-stack-idx))
+         (process-stack (vector-drop-right stack 1) row-idx)]
+        [else 
+         (log-ocm-debug (if (< (vector-length stack) 1) 
+                            (format "row stack too short for challenge, pushing row ~a" row-idx)
+                            (format "challenger row (~a) loses to end of row stack (~a), so ~a joins stack" row-idx (vector-ref stack last-stack-idx) row-idx)))
+         stack])))  
+  
+  (define reduced-row-indexes
+    (for/fold : (Vectorof Index-Type) ([stack (cast (vector) (Vectorof Index-Type))]) ([row-idx (in-vector row-indices)])
+      (let ([stack (process-stack stack row-idx)])
+        (if (= (vector-length stack) (vector-length col-indices))
+            stack
+            ((inst vector-append Index-Type) stack (vector row-idx))))))
+  (log-ocm-debug "finished reduce. row indexes = ~v" reduced-row-indexes)
+  reduced-row-indexes)
+
+(: reduce2 ((Vectorof Index-Type) (Vectorof Index-Type) Matrix-Proc-Type Entry->Value-Type . -> . (Vectorof Index-Type)))
+(define (reduce2 row-indices col-indices matrix-proc entry->value)
+  (let find-survivors ([rows row-indices][survivors : (Listof Index-Type) empty])
+    (cond 
+      [(vector-empty? rows) ((inst list->vector Index-Type) (reverse survivors))]
+      [else
+       (define challenger-row (vector-ref rows 0))
+       (cond
+         ;; no survivors yet, so push first row and keep going
+         [(empty? survivors) (find-survivors (vector-cdr rows) (cons challenger-row survivors))]
+         [else
+          (define index-of-last-survivor (sub1 (length survivors)))
+          (define col-head (vector-ref col-indices index-of-last-survivor))
+          (define-syntax-rule (test-function r) (entry->value (matrix-proc r col-head)))
+          (cond
+            ;; this is the challenge: is the head cell of challenger a new minimum?
+            ;; use < not <=, so the recorded winner is the earliest row with the new minimum, not the latest row
+            ;; if yes, challenger wins. pop element from stack, and let challenger try again (= leave rows alone)
+            [(< (test-function challenger-row) (test-function (car survivors))) (find-survivors rows (cdr survivors))]
+            
+            ;; if not, challenger lost.
+            ;; If we're in the last column, ignore the loser by recurring on the same values
+            [(= col-head (vector-last col-indices)) (find-survivors (vector-cdr rows) survivors)]
+            
+            ;; otherwise challenger lost and we're not in last column, 
+            ;; so add challenger to survivor stack
+            [else (find-survivors (vector-cdr rows) (cons challenger-row survivors))])])])))
+
+;; define a special type so it can be reused in `interpolate`
+;; it is (cons value row-idx)
+(define-type Make-Minimum-Input (Pair Any Index-Type)) 
+(: make-minimum (Make-Minimum-Input . -> . (HashTable Any Any)))
+(define (make-minimum value-rowidx-pair)
+  (define ht ((inst make-hash Any Any)))
+  (! ht 'value (car value-rowidx-pair))
+  (! ht 'row-idx (cdr value-rowidx-pair))
+  ht)
+
+
+;; Interpolate phase: in the minima hash, add results for even rows 
+
+(define-syntax-rule (vector-last v)
+  (vector-ref v (sub1 (vector-length v))))
+
+(: interpolate ((HashTable Any Any) (Vectorof Index-Type) (Vectorof Index-Type) Matrix-Proc-Type Entry->Value-Type . -> . (HashTable Any Any)))
+(define (interpolate minima row-indices col-indices matrix-proc entry->value)
+  ;(hash? vector? vector? procedure? procedure? . -> . hash?)
+  (for ([col-idx (in-range 0 (vector-length col-indices) 2)]) ;; even-col-indices
+    (define col (vector-ref col-indices col-idx))
+    (define idx-of-last-row
+      (cast (if (= col-idx (sub1 (vector-length col-indices)))
+          (vector-last row-indices)
+          (hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))
+    
+    (define smallest-value-entry
+      ((inst vector-argmin Make-Minimum-Input) (λ(x) (entry->value (car x)))
+                     (for/vector : (Vectorof Make-Minimum-Input) 
+                       ([row-idx (in-list ((inst dropf-right Index-Type) (vector->list row-indices) (λ(x) (not (= x idx-of-last-row)))))])
+                       (cons (matrix-proc row-idx col) row-idx))))
+    
+    (! minima col (make-minimum smallest-value-entry)))
+  minima)
+
+(: interpolate2 ((HashTable Any Any) (Vectorof Index-Type) (Vectorof Index-Type) Matrix-Proc-Type Entry->Value-Type . -> . (HashTable Any Any)))
+(define (interpolate2 minima row-indices col-indices matrix-proc entry->value)
+  (define idx-of-last-col (sub1 (vector-length col-indices)))
+  (define (smallest-value-entry [col : Index-Type] [idx-of-last-row : Index-Type])
+    ((inst argmin Make-Minimum-Input) (λ(x) (entry->value (car x)))
+            (for/list ([row-idx (stop-after (in-vector row-indices) (λ(x) (= idx-of-last-row x)))])
+              (cons (matrix-proc row-idx col) row-idx))))
+  
+  (for ([([col : Index-Type] col-idx) (in-indexed col-indices)] #:when (even? col-idx))
+    (define idx-of-last-row (cast (if (= col-idx idx-of-last-col)
+                                (vector-last row-indices)
+                                (hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))   
+    (! minima col (make-minimum (smallest-value-entry col idx-of-last-row))))
+  minima)
+
+
+
+#|
+    Search for the minimum value in each column of a matrix.
+    The return value is a dictionary mapping ColIndices to pairs
+    (value,rowindex). We break ties in favor of earlier rows.
+    
+    The matrix is defined implicitly as a function, passed
+    as the third argument to this routine, where Matrix(i,j)
+    gives the matrix value at row index i and column index j.
+    The matrix must be concave, that is, satisfy the property
+        Matrix(i,j) > Matrix(i',j) => Matrix(i,j') > Matrix(i',j')
+    for every i<i' and j<j'; that is, in every submatrix of
+    the input matrix, the positions of the column minima
+    must be monotonically nondecreasing.
+    
+    The rows and columns of the matrix are labeled by the indices
+    given in order by the first two arguments. In most applications,
+    these arguments can simply be integer ranges.
+|#
+
+;; The return value `minima` is a hash:
+;; the keys are col-indices (integers)
+;; the values are pairs of (value row-index).
+(: concave-minima (((Vectorof Index-Type)) ((Vectorof Index-Type) Matrix-Proc-Type Entry->Value-Type) . ->* . HashTableTop))
+(define (concave-minima row-indices [col-indices (vector)] [matrix-proc (cast (make-caching-proc identity) Matrix-Proc-Type)] [entry->value (cast identity Entry->Value-Type)])
+  ;((vector?) ((or/c #f vector?) procedure? procedure?) . ->* . hash?)
+  (define reduce-proc reduce2)
+  (define interpolate-proc interpolate2)
+  (if (= 0 (vector-length col-indices)) 
+      (make-hash)
+      (let ([row-indices (reduce-proc row-indices col-indices matrix-proc entry->value)])
+        (define odd-column-minima (concave-minima row-indices (cast (vector-odd-elements (cast col-indices (Vectorof Any))) (Vectorof Index-Type)) matrix-proc entry->value))
+        (interpolate-proc (cast odd-column-minima (HashTable Any Any)) row-indices col-indices matrix-proc entry->value))))
+
+
+#|
+    Online concave minimization algorithm of Galil and Park.
+    
+    OnlineConcaveMinima(Matrix,initial) creates a sequence of pairs
+    (self.value(j),self.index(j)), where
+        self.value(0) = initial,
+        self.value(j) = min { Matrix(i,j) | i < j } for j > 0,
+    and where self.index(j) is the value of j that provides the minimum.
+    Matrix(i,j) must be concave, in the same sense as for ConcaveMinima.
+    
+    We never call Matrix(i,j) until value(i) has already been computed,
+    so that the Matrix function may examine previously computed values.
+    Calling value(i) for an i that has not yet been computed forces
+    the sequence to be continued until the desired index is reached.
+    Calling iter(self) produces a sequence of (value,index) pairs.
+    
+    Matrix(i,j) should always return a value, rather than raising an
+    exception, even for j larger than the range we expect to compute.
+    If j is out of range, a suitable value to return that will not
+    violate concavity is Matrix(i,j) = -i.  It will not work correctly
+    to return a flag value such as None for large j, because the ties
+    formed by the equalities among such flags may violate concavity.
+|#
+
+;; Online Concave Minima object
+;(struct $ocm  (values indices finished matrix-proc base tentative) #:transparent #:mutable)
+
+;; State used by self.value(), self.index(), and iter(self) =
+;; $ocm-values, $ocm-indices, $ocm-finished
+
+#|
+State used by the internal algorithm:
+$ocm-matrix, $ocm-base, $ocm-tentative
+
+We allow self._values to be nonempty for indices > finished,
+keeping invariant that
+(1) self._values[i] = Matrix(self._indices[i], i),
+(2) if the eventual correct value of self.index(i) < base,
+    then self._values[i] is nonempty and correct.
+
+In addition, we keep a column index self._tentative, such that
+(3) if i <= tentative, and the eventual correct value of
+    self.index(i) <= finished, then self._values[i] is correct.
+|#
+
+
+(define no-value 'none)
+
+(define-syntax-rule (@ hashtable key)
+  (hash-ref hashtable key))
+
+(define-syntax-rule (! hashtable key value)
+  (hash-set! hashtable key value))
+
+(: ocm-ref (OCM-Type Index-Type . -> . Any)) 
+(define (ocm-ref ocm key)
+  (vector-ref ocm key))
+
+(: ocm-set! (OCM-Type Index-Type Any . -> . Void)) 
+(define (ocm-set! ocm key value)
+  (vector-set! ocm key value))
+
+(define-type OCM-Type (Vector Any Any Any Any Any Any Any))
+(define-type Index-Type Nonnegative-Integer)
+(define-type Matrix-Proc-Type (Index-Type Index-Type . -> . Any))
+(define-type Entry->Value-Type (Any . -> . Flonum))
+(define-type Indices-Type (Vectorof Index-Type))
+
+ 
+(define o:min-values 0)
+(define o:min-row-indices 1)
+(define o:finished 2)
+(define o:matrix-proc 3)
+(define o:entry->value 4)
+(define o:base 5)
+(define o:tentative 6)
+
+(: make-ocm ((Procedure) (Any Procedure) . ->* . OCM-Type))
+(define (make-ocm matrix-proc [initial-value 0][entry->value identity])
+  (log-ocm-debug "making new ocm")
+  (define ocm (cast (make-vector 7) OCM-Type))
+  (ocm-set! ocm o:min-values (vector initial-value))
+  (ocm-set! ocm o:min-row-indices (vector no-value))
+  (ocm-set! ocm o:finished 0)
+  (ocm-set! ocm o:matrix-proc (make-caching-proc matrix-proc))
+  (ocm-set! ocm o:entry->value entry->value) ; for converting matrix values to an integer
+  (ocm-set! ocm o:base 0)
+  (ocm-set! ocm o:tentative 0)
+  (cast ocm OCM-Type))
+
+;; Return min { Matrix(i,j) | i < j }.
+(: min-value (OCM-Type Index-Type . -> . Any))
+(define (min-value ocm j)
+  (if (< (cast (ocm-ref ocm o:finished) Real) j)
+      (begin (advance! ocm) (min-value ocm j))
+      (vector-ref (cast (ocm-ref ocm o:min-values) VectorTop) j)))
+
+;; Return argmin { Matrix(i,j) | i < j }.
+(: min-index (OCM-Type Index-Type . -> . Index-Type))
+(define (min-index ocm j)
+  (if (< (cast (ocm-ref ocm o:finished) Real) j)     
+      (begin (advance! ocm) (min-index ocm j))
+      ((inst vector-ref Index-Type) (cast (ocm-ref ocm o:min-row-indices) (Vectorof Index-Type)) j)))
+
+;; Finish another value,index pair.
+(: advance! (OCM-Type . -> . Void))
+(define (advance! ocm)
+  (define next (add1 (cast (ocm-ref ocm o:finished) Index-Type)))  
+  (log-ocm-debug "advance! ocm to next = ~a" (add1 (cast (ocm-ref ocm o:finished) Number)))
+  (cond
+    ;; First case: we have already advanced past the previous tentative
+    ;; value.  We make a new tentative value by applying ConcaveMinima
+    ;; to the largest square submatrix that fits under the base.
+    [(> next (cast (ocm-ref ocm o:tentative) Real))
+     (log-ocm-debug "advance: first case because next (~a) > tentative (~a)" next (ocm-ref ocm o:tentative))
+     (define rows : (Vectorof Index-Type) (list->vector (range (cast (ocm-ref ocm o:base) Index-Type) next)))
+     (ocm-set! ocm o:tentative (+ (cast (ocm-ref ocm o:finished) Number) (vector-length rows)))
+     (define cols : (Vectorof Index-Type) (list->vector (range next (add1 (cast (ocm-ref ocm o:tentative) Index-Type)))))
+     (define minima (concave-minima rows cols (cast (ocm-ref ocm o:matrix-proc) Matrix-Proc-Type) (cast (ocm-ref ocm o:entry->value) Entry->Value-Type)))
+     (for ([col (in-vector cols)])
+       (cond
+         [(>= col (vector-length (cast (ocm-ref ocm o:min-values) VectorTop)))
+          (ocm-set! ocm o:min-values (vector-append-item (ocm-ref ocm o:min-values) (@ (cast (@ minima col) HashTableTop) 'value)))
+          (ocm-set! ocm o:min-row-indices (vector-append-item (ocm-ref ocm o:min-row-indices) (@ (@ minima col) 'row-idx)))]
+         [(< ((ocm-ref ocm o:entry->value) (@ (@ minima col) 'value)) ((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) col)))
+          (ocm-set! ocm o:min-values (vector-set (ocm-ref ocm o:min-values) col (@ (@ minima col) 'value)))
+          (ocm-set! ocm o:min-row-indices (vector-set (ocm-ref ocm o:min-row-indices) col (@ (@ minima col) 'row-idx)))]))
+     (ocm-set! ocm o:finished next)]
+    
+    [else
+     ;; Second case: the new column minimum is on the diagonal.
+     ;; All subsequent ones will be at least as low,
+     ;; so we can clear out all our work from higher rows.
+     ;; As in the fourth case, the loss of tentative is
+     ;; amortized against the increase in base.
+     (define diag ((ocm-ref ocm o:matrix-proc) (sub1 next) next))
+     (cond
+       [(< ((ocm-ref ocm o:entry->value) diag) ((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) next)))
+        (log-ocm-debug "advance: second case because column minimum is on the diagonal")
+        (ocm-set! ocm o:min-values (vector-set (ocm-ref ocm o:min-values) next diag))
+        (ocm-set! ocm o:min-row-indices (vector-set (ocm-ref ocm o:min-row-indices) next (sub1 next)))
+        (ocm-set! ocm o:base (sub1 next))
+        (ocm-set! ocm o:tentative next)
+        (ocm-set! ocm o:finished next)]
+       
+       ;; Third case: row i-1 does not supply a column minimum in
+       ;; any column up to tentative. We simply advance finished
+       ;; while maintaining the invariant.
+       [(>= ((ocm-ref ocm o:entry->value) ((ocm-ref ocm o:matrix-proc) (sub1 next) (ocm-ref ocm o:tentative)))
+            ((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) (ocm-ref ocm o:tentative))))
+        (log-ocm-debug "advance: third case because row i-1 does not suppply a column minimum")
+        (ocm-set! ocm o:finished next)]
+       
+       ;; Fourth and final case: a new column minimum at self._tentative.
+       ;; This allows us to make progress by incorporating rows
+       ;; prior to finished into the base.  The base invariant holds
+       ;; because these rows cannot supply any later column minima.
+       ;; The work done when we last advanced tentative (and undone by
+       ;; this step) can be amortized against the increase in base.
+       [else
+        (log-ocm-debug "advance: fourth case because new column minimum")
+        (ocm-set! ocm o:base (sub1 next))
+        (ocm-set! ocm o:tentative next)
+        (ocm-set! ocm o:finished next)])]))
\ No newline at end of file