Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Cluster adjacency beyond MHV

Abstract: We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $$ \overline{Q} $$ -equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.

Open problems in the spectral theory of signed graphs

Abstract: Signed graphs are graphs whose edges get a sign +1 or −1 (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much attention from graph spectra specialists. One motivation is that the spectral theory of signed graphs elegantly generalizes the spectral theories of unsigned graphs. On the other hand, unsigned graphs do not disappear completely, since their role can be taken by the special case of balanced signed graphs. Therefore, spectral problems defined and studied for unsigned graphs can be considered in terms of signed graphs, and sometimes such generalization shows nice properties which cannot be appreciated in terms of (unsigned) graphs. Here, we survey some general results on the adjacency spectra of signed graphs, and we consider some spectral problems which are inspired from the spectral theory of (unsigned) graphs.

Testing Expansion in Bounded-Degree Graphs

Abstract: We consider the problem of testing expansion in bounded degree graphs. We focus on the notion of vertex-expansion: an alpha-expander is a graph G = (V, E) in which even-subset U sube V of at most |V|/2 vertices has a neighborhood of size at least alphaldr|U|. Our main result is that one can distinguish good expanders from graphs that are far from being weak expanders in time O tilde(radicn). We prove that the property testing algorithm proposed by Goldreich and Ron (2000) with appropriately set parameters accepts every alpha-expander with probability at least 2/3 and rejects every graph that is epsiv-far from an alpha*-expander with probability at least 2/3, where alpha*=Theta(alpha2/(d2log (n/epsiv))) and d is the maximum degree of the graphs. The algorithm assumes the bounded-degree graphs model with adjacency list graph representation and its running time is O(d2(radicn log (n/epsiv))/alpha2epsiv3).

Cut, Glue, & Cut: A Fast, Approximate Solver for Multicut Partitioning

Abstract: Recently, unsupervised image segmentation has become increasingly popular. Starting from a superpixel segmentation, an edge-weighted region adjacency graph is constructed. Amongst all segmentations of the graph, the one which best conforms to the given image evidence, as measured by the sum of cut edge weights, is chosen. Since this problem is NP-hard, we propose a new approximate solver based on the move-making paradigm: first, the graph is recursively partitioned into small regions (cut phase). Then, for any two adjacent regions, we consider alternative cuts of these two regions defining possible moves (glue & cut phase). For planar problems, the optimal move can be found, whereas for non-planar problems, efficient approximations exist. We evaluate our algorithm on published and new benchmark datasets, which we make available here. The proposed algorithm finds segmentations that, as measured by a loss function, are as close to the ground-truth as the global optimum found by exact solvers. It does so significantly faster then existing approximate methods, which is important for large-scale problems.

A scalable, distributed algorithm for efficient task allocation

Abstract: We present a distributed algorithm for task allocation in multi-agent systems for settings in which agents and tasks are geographically dispersed in two-dimensional space. We describe a method that enables agents to determine individually how to move so that they are, as a group, efficiently assigned to tasks. The method comprises two algorithms and is especially useful in environments with very large numbers of agent and task nodes. One algorithm adapts computational geometry techniques to determine adjacency information for the agent nodes given the geographical positions of agents and tasks. This adjacency information is used to determine the visible nodes that are most relevant to an agent's decision making process and to eliminate those that it should not consider. The second algorithm uses local heuristics based solely on an agent's adjacent nodes to determine its course of action. This method yields improved task allocations compared to previous algorithms proposed for similar environments. We also present a modification to the second algorithm that improves performance in environments in which multiple agents are required to complete a single task.