Faster Algebraic Algorithms for Path and Packing Problems

Koutis, Ioannis

doi:10.1007/978-3-540-70575-8_47

Cited by 163 publications

(227 citation statements)

References 12 publications

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“…The exist methods mostly use the color-coding technique to find loop with logarithmic length, if they exist. Using color-coding, the dependence on path length can be reduced to singly exponential [2,6,19,27]. But this gives an approximation ratio of only O(n/ log n) [2].…”

Section: Cheating Algorithm Based On Hllsbdmentioning

confidence: 99%

Cooperative Game-based Cheating in Full-duplex Relaying-based D2D Communication Underlaying Heterogeneous Cellular Networks

et al. 2017

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Device-to-device (D2D) communications allow direct transmissions between two adjacent user devices, which can improve system performance in cellular networks. Considering full-duplex (FD) relaying outperforms half-duplex (HD) relaying in spectrum and energy efficiency, we apply the FD relaying-based D2D communication scheme in heterogeneous cellular network, which allows D2D links to underlay cellular downlink by assigning D2D transmitters as FD relays to assist cellular downlink transmissions. Although the scheme can improve the utilization of spectrum resource dramatically, the unreasonable resource sharing of D2D users will increase the inter-user interference. Therefore, in this paper, we try to optimize the throughput of D2D users on the premise of ensuring the quality of service (QoS) of cellular users. To this end, we first propose a D2D transmit power-allocation scheme and use Gale-Sharpley (GS) algorithm in matching theory to solve the resource allocation problem. Next, a Cheating algorithm based on cooperative game theory is proposed to further improve the throughput of D2D users. More importantly, due to the NP-hardness of finding the optimal solution of Cheating algorithm, we propose a heuristic algorithm based on depth first search (DFS) which using different colors to represent the different statements of D2D users to find a near-optimal solution. The simulation results show that the proposed algorithm compared with GS algorithm can significantly improve the total throughput of D2D users, and it also has lower complexity and better throughput performance against existing Cheating algorithm.

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Section: Cheating Algorithm Based On Hllsbdmentioning

confidence: 99%

Cooperative Game-based Cheating in Full-duplex Relaying-based D2D Communication Underlaying Heterogeneous Cellular Networks

et al. 2017

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“…Our present design framework, constrained multilinear sieving, originates from seminal work of Koutis [31], Williams [48], Koutis and Williams [33], and Koutis [32] in the context of group algebras. However, rather than work with group algebras we find it more convenient to pursue an implementation via multivariate polynomials and inclusion-exclusion sieving by polynomial substitution [4,5,6,7].…”

Section: Motivation and Earliermentioning

confidence: 99%

Engineering Motif Search for Large Graphs

Björklund

Kaski

Kowalik

et al. 2014

2015 Proceedings of the Seventeenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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In the graph motif problem, we are given as input a vertexcolored graph H (the host graph) and a multiset of colors M (the motif). Our task is to decide whether H has a connected set of vertices whose multiset of colors agrees with M . The graph motif problem is NP-complete but known to admit parameterized algorithms that run in linear time in the size of H. We demonstrate that algorithms based on constrained multilinear sieving are viable in practice, scaling to graphs with hundreds of millions of edges as long as M remains small. Furthermore, our implementation is topologyinvariant relative to the host graph H, meaning only the most crude graph parameters (number of edges and number of vertices) suffice in practice to determine the algorithm performance.

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“…Algorithm Exact uses a non-trivial combination of narrow sieves [4] (see also [22]) and divide-and-color [10], which are often applied as two independent tools in the development of parameterized algorithms. Narrow sieves is an algebraic technique in which we express a parameterized problem by associating monomials with potential solutions.…”

Section: An Overview Of Our Algorithmsmentioning

confidence: 99%

Improved Parameterized Algorithms for Network Query Problems

Pinter

Shachnai

Zehavi

2014

Parameterized and Exact Computation

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Abstract. Biological networks are often explored through extensive use of network queries. Partial Information Network Queries (PINQ) address the major challenge of analyzing such networks in the absence of certain topological data. In the PINQ problem, we are given a host graph H, modeling a network, and a pattern P, whose topology is only partially known. We seek a subgraph of H that resembles P. In this paper, we study a generalization of PINQ which allows near resemblance between H and P. We obtain an exact parameterized algorithm as well as an FPT-approximation scheme for a wide class of inputs, where the parameter is the number of nodes in P. Our algorithms substentially improve the best O * running times in solving PINQ, as well as the special cases of the Alignment Network Query problem and the Topology-Free Network Query problem.

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Faster Algebraic Algorithms for Path and Packing Problems

Cited by 163 publications

References 12 publications

Cooperative Game-based Cheating in Full-duplex Relaying-based D2D Communication Underlaying Heterogeneous Cellular Networks

Cooperative Game-based Cheating in Full-duplex Relaying-based D2D Communication Underlaying Heterogeneous Cellular Networks

Engineering Motif Search for Large Graphs

Improved Parameterized Algorithms for Network Query Problems

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