**Abstract:**
Efficient
allocation
of
tasks
to
workers
is
a
central
problem
in
crowdsourcing.
In
a
typical
setting,
different
workers
arrive
at
different
times.
Similarly,
different
tasks
arrive
at
different
times.
The
goal
is
to
assign
the
available
workers
to
tasks,
such
that
we
are
able
to
complete
as
many
tasks
as
possible.
Usually,
the
tasks
are
heterogeneous
and
have
different
rewards.
Hence,
we
would
like
to
maximize
the
total
reward
(as
opposed
to
just
the
number
of
completed
tasks).
Often,
the
arrival
times
of
worker
"types"
and
task
"types"
are
not
erratic
and
can
be
predicted
from
historical
data.
In
this
paper,
we
model
the
problem
to
account
for
this
history
and
propose
a
new
mathematical
model,
called
Online
Matching
with
Two-Sided
Arrival
(OM-TSA).
We
have
a
known
bipartite
graph
G
=
(U,V,E)
where
U
is
the
set
of
worker
types
and
V
is
the
set
of
task
types.
An
edge
e
=
(u,
v)
exists
iff
worker
u
is
compatible
with
task
v.
The
setting
proceeds
in
rounds
for
T
time-steps.
At
each
time-step,
a
worker
u
from
U
and
a
task
v
from
V
are
sampled
independently
from
two
respective
(known)
distributions.
Further,
we
assume
the
sampling
processes
are
independent
and
identical
across
the
T
rounds.
We
assume
that
(1)
when
a
worker
u
arrives,
they
stay
in
the
sys-
tem
until
matched
and
(2)
when
a
task
v
arrives,
it
needs
to
be
assigned
to
an
available
worker
u
immediately
(and
obtaining
a
reward
w(u,
v));
if
not,
we
do
not
get
any
reward
for
this
task
(and
the
action
is
irrevocable).
Our
goal
is
to
maximize
the
expected
reward.
Our
model
is
a
significant
generalization
of
the
classical
online
matching
model,
where
one
of
the
sets
U
and
V
,
say
U,
is
assumed
to
be
available
offline.
We
relax
this
assumption
to
capture
the
transient
nature
of
worker
arrivals.
For
the
general
version
of
OM-TSA,
we
present
an
optimal
non-adaptive
algorithm
which
achieves
an
online
competitive
ratio
of
0.295.
For
the
special
case
of
OM-TSA
where
the
reward
is
a
function
of
just
the
worker
type,
we
present
an
improved
algorithm
(which
is
adaptive)
and
achieves
a
competitive
ratio
of
at
least
0.345.
On
the
hardness
side,
along
with
showing
that
the
ratio
obtained
by
our
non-adaptive
algorithm
is
the
best
possible
among
all
non-adaptive
algorithms,
we
further
show
that
no
(adaptive)
algorithm
can
achieve
a
ratio
better
than
0.581
(unconditionally),
even
for
the
special
case
of
OM-TSA
with
homogenous
tasks
(i.e.,
all
rewards
are
same).
At
the
heart
of
our
analysis
lies
a
new
technical
tool
(which
is
a
refined
notion
of
the
birth-death
process)
called
the
two-stage
birth-death
process,
which
may
be
of
independent
interest.
Finally,
we
perform
numerical
experiments
on
both
simulated
as
well
as
two
real-world
datasets
obtained
from
crowdsourcing
platforms
to
complement
our
theoretical
results.

**Keywords:**
Randomized
Algorithms;
Online
Algorithms;
Artificial
Intelligence;
Applications