Hassan Gobjuka

Ethernet topology discovery for networks with incomplete information

In this paper we investigate the problem of finding a layer-2 network topology when the information available from SNMP MIB is incomplete. We prove that finding a network topology in this case is NP-hard. We further prove that deciding whether the given information defines a unique network topology is a co-NP-hard problem. We show that if there is a single node r such that every other network node sees it, then the network topology can be discovered in polynomial (in the number of network ports) time. Finally, we design a polynomial time heuristic algorithm to discover a topology when the information available from SNMP MIB is incomplete and conduct extensive experiments with it to determine how often the algorithm succeeds in finding topology. Our results indicate that our algorithm discovers the network topology in close to 100% of all test cases.

Effective network monitoring

Various network monitoring and performance evaluation schemes generate considerable amount of traffic, which affects network performance. In this paper we describe a method for minimizing network monitoring overhead based on shortest path tree (SPT) protocol. We describe two different variations of the problem: the A-problem and the E-problem, and show that there is a significant difference between them. We prove that finding optimal solutions is NP-hard for both variations, and propose a theoretically best possible heuristic for the A-problem and three different heuristics for the E-problem, one of them being also theoretically best possible. We show that one can compute in polynomial time an O(ln|V|)-approximate solution for each of these problems. Then, we analyze the performance of our heuristics on large graphs generated using Waxman and power-law models as well as on real ISP topology maps. Experiment results show more than 80% improvement when using our heuristics on real topologies over the naive approaches

Ethernet Topology Discovery for Networks with Incomplete Information

In this paper we investigate the problem of finding a layer-2 network topology when the information available from SNMP MIB is incomplete. We prove that finding a network topology in this case is NP-hard. We further prove that deciding whether the given information defines a unique network topology is a co-NP-hard problem. We show that if there is a single node r such that every other network node sees it, then the network topology can be discovered in polynomial (in the number of network ports) time. Finally, we design a polynomial time heuristic algorithm to discover a topology when the information available from SNMP MIB is incomplete and conduct extensive experiments with it to determine how often the algorithm succeeds in finding topology. Our results indicate that our algorithm discovers the network topology in close to 100% of all test cases.

Discovering Network Topology of Large Multisubnet Ethernet Networks

In this paper we investigate the problem of finding the physical layer network topology of large, heterogeneous multisubnet Ethernet networks that may include uncooperative network elements. Our approach utilizes only generic MIB information and does not require any hardware or software modifications of the underlying network elements. We propose here the first O(n3) algorithm that guarantees discovering a topology that is compatible with the given set of input MIBs, provided that the input is complete. We prove the correctness of the algorithms and the necessary and sufficient conditions for the uniqueness of the restored topology. Finally, we demonstrate the application of the algorithm on several examples.

Forwarding-loop-free configuration for IBGP networks

We investigate the inter-cluster routing deflection and forwarding loops in IBGP networks. In more detail, we define and explore the two causes of deflection, and consecutively, forwarding loops which might happen due to IBGP cluster misconfiguration. We study the methods that can be used to remove forwarding loops, if detected. Unfortunately, we show that detecting forwarding loops in a given IBGP network configuration is NP-hard. However, we propose a simple heuristic algorithm with complexity of 0(2) to configure deflection- and loop-free IBGP network.

Topology Discovery for Virtual Local Area Networks

In this paper we investigate the problem of finding the physical layer topology of large, heterogeneous networks that comprises multiple VLANs and may include uncooperative network nodes. We prove that finding a layer-2 network topology for a given incomplete input is an NP-hard problem even when the network comprises only two VLANs and the network contains one loop and deciding whether a given input defines a unique VLANs topology is a co-NP-hard problem. We design several heuristic algorithms to find VLANs topology. Our first algorithm is designed for geographically wide-spread networks that may contain uncooperative devices. For such networks the algorithm discovers the topology for each VLAN then merges them to infer the network topology in O(n^3) time, where

Effective Monitor Placement in Internet Networks

n

Characterization of layer-2 unique topologies

is the number of internal network nodes. Our second algorithm is designed for smaller, active networks where each device in the network provides access to their MIB and few AFT entries are missing. For such networks, the algorithm finds the unique topology of VLANs in O(n^3) time. We have implemented both the algorithms described in this paper and conducted extensive experiments on multiple networks. Our experiments demonstrate that our approach is quite practical and discovers the accurate VLANs topology of large and heterogeneous networks whose input may not necessarily be complete. To the best of our knowledge, this is the first paper investigating topology discovery for VLANs.

Characterization of Layer-2 Unique Topologies in Multisubnet Local Area Networks

Various network monitoring and performance evaluation schemes generate considerable amount of traf- fic, which affects network performance. In this paper we describe a method for minimizing network monitoring overhead based on Shortest Path Tree (SPT) protocol. We describe two different variations of the problem: the A Problem and the E -Problem and prove that finding optimal solutions for both A - and E -problems is NP -hard. We also show that in general, an A -problem solution requires a significantly higher network overhead than an E -problem solution. We propose optimal approximation algorithms for the A - and E -problems and few different heuristics for the E -problem. Namely, we show that one can compute in polynomial time an O(ln|V |) -approximate solution for each of these problems. We analyze the performance of our approximation algorithms and heuristics on large graphs generated using Power-Law model. Performance results show that our heuristic algorithms for both problems achieve from 50% to 90% improvement in the network overhead comparatively with earlier algorithms that appeared in literature.

Fast and scalable method for resolving anomalies in firewall policies

In this paper we study a layer-2 topology restoration for multisubnet networks. We design a new algorithm for generating such topologies and prove a criterion on a set of input data that guarantees a unique layer-2 topology. Our criterion is easily verifiable in O(n^2) time, where n is the number of internal network nodes.