7,946 research outputs found
Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity
In bipartite matching problems, vertices on one side of a bipartite graph are
paired with those on the other. In its online variant, one side of the graph is
available offline, while the vertices on the other side arrive online. When a
vertex arrives, an irrevocable and immediate decision should be made by the
algorithm; either match it to an available vertex or drop it. Examples of such
problems include matching workers to firms, advertisers to keywords, organs to
patients, and so on. Much of the literature focuses on maximizing the total
relevance---modeled via total weight---of the matching. However, in many
real-world problems, it is also important to consider contributions of
diversity: hiring a diverse pool of candidates, displaying a relevant but
diverse set of ads, and so on. In this paper, we propose the Online Submodular
Bipartite Matching (\osbm) problem, where the goal is to maximize a submodular
function over the set of matched edges. This objective is general enough to
capture the notion of both diversity (\emph{e.g.,} a weighted coverage
function) and relevance (\emph{e.g.,} the traditional linear function)---as
well as many other natural objective functions occurring in practice
(\emph{e.g.,} limited total budget in advertising settings). We propose novel
algorithms that have provable guarantees and are essentially optimal when
restricted to various special cases. We also run experiments on real-world and
synthetic datasets to validate our algorithms.Comment: To appear in AAAI 201
Bi-Criteria and Approximation Algorithms for Restricted Matchings
In this work we study approximation algorithms for the \textit{Bounded Color
Matching} problem (a.k.a. Restricted Matching problem) which is defined as
follows: given a graph in which each edge has a color and a profit
, we want to compute a maximum (cardinality or profit)
matching in which no more than edges of color are
present. This kind of problems, beside the theoretical interest on its own
right, emerges in multi-fiber optical networking systems, where we interpret
each unique wavelength that can travel through the fiber as a color class and
we would like to establish communication between pairs of systems. We study
approximation and bi-criteria algorithms for this problem which are based on
linear programming techniques and, in particular, on polyhedral
characterizations of the natural linear formulation of the problem. In our
setting, we allow violations of the bounds and we model our problem as a
bi-criteria problem: we have two objectives to optimize namely (a) to maximize
the profit (maximum matching) while (b) minimizing the violation of the color
bounds. We prove how we can "beat" the integrality gap of the natural linear
programming formulation of the problem by allowing only a slight violation of
the color bounds. In particular, our main result is \textit{constant}
approximation bounds for both criteria of the corresponding bi-criteria
optimization problem
Strong Structural Controllability of Systems on Colored Graphs
This paper deals with structural controllability of leader-follower networks.
The system matrix defining the network dynamics is a pattern matrix in which a
priori given entries are equal to zero, while the remaining entries take
nonzero values. The network is called strongly structurally controllable if for
all choices of real values for the nonzero entries in the pattern matrix, the
system is controllable in the classical sense. In this paper we introduce a
more general notion of strong structural controllability which deals with the
situation that given nonzero entries in the system's pattern matrix are
constrained to take identical nonzero values. The constraint of identical
nonzero entries can be caused by symmetry considerations or physical
constraints on the network. The aim of this paper is to establish graph
theoretic conditions for this more general property of strong structural
controllability.Comment: 13 page
Streaming Verification of Graph Properties
Streaming interactive proofs (SIPs) are a framework for outsourced
computation. A computationally limited streaming client (the verifier) hands
over a large data set to an untrusted server (the prover) in the cloud and the
two parties run a protocol to confirm the correctness of result with high
probability. SIPs are particularly interesting for problems that are hard to
solve (or even approximate) well in a streaming setting. The most notable of
these problems is finding maximum matchings, which has received intense
interest in recent years but has strong lower bounds even for constant factor
approximations.
In this paper, we present efficient streaming interactive proofs that can
verify maximum matchings exactly. Our results cover all flavors of matchings
(bipartite/non-bipartite and weighted). In addition, we also present streaming
verifiers for approximate metric TSP. In particular, these are the first
efficient results for weighted matchings and for metric TSP in any streaming
verification model.Comment: 26 pages, 2 figure, 1 tabl
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