Search

Deep models deployed on edge devices frequently encounter resource variability, which arises from fluctuating energy levels, timing constraints, or prioritization of other critical tasks within the system. State-of-the-art machine learning pipelines generate resource-agnostic models, not capable to adapt at runtime. In this work we introduce Resource-Efficient Deep Subnetworks (REDS) to tackle model adaptation to variable resources. In contrast to the state-of-the-art, REDS use structured sparsity constructively by exploiting permutation invariance of neurons, which allows for hardware-specific optimizations. Specifically, REDS achieve computational efficiency by (1) skipping sequential computational blocks identified by a novel iterative knapsack optimizer, and (2) leveraging simple math to re-arrange the order of operations in REDS computational graph to take advantage of the data cache. REDS support conventional deep networks frequently deployed on the edge and provide computational benefits even for small and simple networks. We evaluate REDS on seven benchmark architectures trained on the Visual Wake Words, Google Speech Commands, Fashion-MNIST and CIFAR10 datasets, and test on four off-the-shelf mobile and embedded hardware platforms. We provide a theoretical result and empirical evidence for REDS outstanding performance in terms of submodels' test set accuracy, and demonstrate an adaptation time in response to dynamic resource constraints of under 40$\mu$s, utilizing a 2-layer fully-connected network on Arduino Nano 33 BLE.

We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent incompatible pairs of items which should not be allocated to the same agent. This setting combines the issues of Partition and Independent Set and can be seen as a partial coloring of the conflict graph. In the resulting optimization problem each agent has its own valuation function for the profits of the items. We aim at maximizing the lowest total profit obtained by any of the agents. In a previous paper this problem was shown to be strongly \NP-hard for several well-known graph classes, e.g., bipartite graphs and their line graphs. On the other hand, it was shown that pseudo-polynomial time algorithms exist for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. In this contribution we extend this line of research by developing pseudo-polynomial time algorithms that solve the problem for the class of convex bipartite conflict graphs, graphs of bounded clique-width, and graphs of bounded tree-independence number. The algorithms are based on dynamic programming and also permit fully polynomial-time approximation schemes (FPTAS).

We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to this classical problem. Namely, we introduce an incompatibility relation between pairs of items described in terms of a conflict graph. Every subset of items assigned to one agent has to form an independent set in this graph. Thus, the allocation of items to the agents corresponds to a partial coloring of the conflict graph. Every agent has its own profit valuation for every item. Aiming at a fair allocation, our goal is the maximization of the lowest total profit of items allocated to any one of the agents. The resulting optimization problem contains, as special cases, both Partition and Independent Set. In our contribution we derive complexity and algorithmic results depending on the properties of the given graph. We show that the problem is strongly NP-hard for bipartite graphs and their line graphs, and solvable in pseudo-polynomial time for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. Each of the pseudo-polynomial algorithms can also be turned into a fully polynomial approximation scheme (FPTAS)., Comment: A preliminary version containing some of the results presented here appeared in the proceedings of IWOCA 2020

We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We show that this recently introduced variant of the knapsack problem is weakly NP-hard and present a fully polynomial-time approximation scheme (FPTAS) for the problem. Moreover, we analyze the approximation quality achieved by a natural extension of the classical greedy procedure to the product knapsack problem.

The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G, called the guest graph, to the leaves of a d-regular tree T, called the host graph, such that the sum of the pairwise distances of all pairs of leaves in T which correspond to the edges of G is minimised. Luczak and Noble have shown that this problem is NP-hard for every fixed d greater than or equal to 2. In this paper we show that the DAPT remains NP-hard even if the guest graph is a tree, an issue which was posed as an open question in by Luczak and Noble. We deal with a special case of the DAPT where both the guest and the host graph are binary regular trees and provide a 1.015-approximation algorithm for this special case. The solution produced by the algorithm and the corresponding value of the objective function are given in closed form. The analysis of the approximation algorithm involves an auxiliary problem which is interesting on its own, namely the k-balanced partitioning problem (kBPP) for binary regular trees and particular choices of k. We derive a lower bound for the later problem and obtain a lower bound for the original problem by solving hG instances of the k-BPP, where hG is the height of the host graph G.

We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently located at. In this way, each of the players forms a path that origins from its respective starting vertex. The game ends as soon as the two paths meet, i.e., a connection between the players is established. Each player has to carry the cost of its chosen edges and thus aims at minimizing its own total cost. In this work we analyze the computational complexity of Shortest Connection Game. On the negative side, the game turns out to be computationally hard even on restricted graph classes such as bipartite, acyclic and cactus graphs. On the positive side, we can give a polynomial time algorithm for cactus graphs when the game is restricted to simple paths.

In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns in deciding in each vertex which edge to traverse next. The decider in each vertex also has to pay the cost of the chosen edge. We want to determine the path where each player minimizes its costs taking into account that also the other player acts in a selfish and rational way. Such a solution is a subgame perfect equilibrium and can be determined by backward induction in the game tree of the associated finite game in extensive form. We show that the decision problem associated with such a path is PSPACE-complete even for bipartite graphs both for the directed and the undirected version. The latter result is a surprising deviation from the complexity status of the closely related game Geography. On the other hand, we can give polynomial time algorithms for directed acyclic graphs and for cactus graphs even in the undirected case. The latter is based on a decomposition of the graph into components and their resolution by a number of fairly involved dynamic programming arrays. Finally, we give some arguments about closing the gap of the complexity status for graphs of bounded treewidth., Comment: Extended version contains the full description of the dynamic programming arrays in Section 4

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model, where agents' preferences are binary, i.e., each agent classifies all pairs of the form "(activity, group size)" into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents' preferences satisfy certain natural constraints., Comment: 13 pages, presented at WINE-2012 and COMSOC-2012