750 research outputs found
Non-additive Security Games
We have investigated the security game under non-additive utility functions
Public projects, Boolean functions and the borders of Border's theorem
Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. This paper identifies a
complexity-theoretic barrier that indicates, assuming standard complexity class
separations, that Border's theorem cannot be extended significantly beyond the
state-of-the-art. We also identify a surprisingly tight connection between
Myerson's optimal auction theory, when applied to public project settings, and
some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201
2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties
The solution to a Nash or a nonsymmetric bargaining game is obtained by
maximizing a concave function over a convex set, i.e., it is the solution to a
convex program. We show that each 2-player game whose convex program has linear
constraints, admits a rational solution and such a solution can be found in
polynomial time using only an LP solver. If in addition, the game is succinct,
i.e., the coefficients in its convex program are ``small'', then its solution
can be found in strongly polynomial time. We also give a non-succinct linear
game whose solution can be found in strongly polynomial time
Optimality of Treating Interference as Noise: A Combinatorial Perspective
For single-antenna Gaussian interference channels, we re-formulate the
problem of determining the Generalized Degrees of Freedom (GDoF) region
achievable by treating interference as Gaussian noise (TIN) derived in [3] from
a combinatorial perspective. We show that the TIN power control problem can be
cast into an assignment problem, such that the globally optimal power
allocation variables can be obtained by well-known polynomial time algorithms.
Furthermore, the expression of the TIN-Achievable GDoF region (TINA region) can
be substantially simplified with the aid of maximum weighted matchings. We also
provide conditions under which the TINA region is a convex polytope that relax
those in [3]. For these new conditions, together with a channel connectivity
(i.e., interference topology) condition, we show TIN optimality for a new class
of interference networks that is not included, nor includes, the class found in
[3].
Building on the above insights, we consider the problem of joint link
scheduling and power control in wireless networks, which has been widely
studied as a basic physical layer mechanism for device-to-device (D2D)
communications. Inspired by the relaxed TIN channel strength condition as well
as the assignment-based power allocation, we propose a low-complexity
GDoF-based distributed link scheduling and power control mechanism (ITLinQ+)
that improves upon the ITLinQ scheme proposed in [4] and further improves over
the heuristic approach known as FlashLinQ. It is demonstrated by simulation
that ITLinQ+ provides significant average network throughput gains over both
ITLinQ and FlashLinQ, and yet still maintains the same level of implementation
complexity. More notably, the energy efficiency of the newly proposed ITLinQ+
is substantially larger than that of ITLinQ and FlashLinQ, which is desirable
for D2D networks formed by battery-powered devices.Comment: A short version has been presented at IEEE International Symposium on
Information Theory (ISIT 2015), Hong Kon
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